In the Old Testament, many figures are types, or foreshadowings, of Christ. Some of these types are more familiar to Catholics than others. I think Joshua* is one of the lesser-known types for Catholics. It’s a shame, as there any number of obvious parallels:
–In Hebrew and Greek, the names Joshua and Jesus are the same. Jesus is the new Joshua.
–Joshua led the old Chosen People into the Promised Land after the death of Moses. Jesus leads the new Chosen People into Heaven after the death of the Mosaic Law. What Joshua is in the Old Testament, Jesus is in the New Testament.
–Joshua leads the Israelites through the Jordan River into the Promised Land. Christ was baptized in the Jordan, and Baptism opens the gates of Heaven to us.
Catholic, Protestant, and presumably (?) Orthodox scholars have assembled these parallels and others to boot. I propose a parallel that I’ve never seen called out elsewhere: Joshua’s last words foreshadow Christ’s institution of the Papacy.
With Stone as My Witness . . .
To set the scene, Joshua has come to the end of his life and is delivering his final speech to the Israelites (Joshua chapters 23-24). He makes a covenant with them. He commits the Israelites to the Lord, and he forbids them to worship idols. One of his lines is, “But as for me and my house, we will serve the LORD” (Joshua 24:15), which I’ve seen on a wall-hanging in the house of a Methodist family I know. At the conclusion of the speech, Joshua does something interesting to seal his covenant: he makes a stone his witness (Joshua 24:26-27):
“ And he [Joshua] wrote all these things in the volume of the law of the Lord: and he took a great stone, and set it under the oak that was in the sanctuary of the Lord.  And he said to all the people: Behold this stone shall be a testimony [in the Greek, martyrion] unto you, that it hath heard all the words of the Lord, which he hath spoken to you: lest perhaps hereafter you will deny it, and lie to the Lord your God.”
Do you see how this scene foreshadows Christ and St. Peter, the first Pope? Jesus, the new Joshua, made a New Covenant with the Church, which is the New Israel. He established the terms of the covenant, which included commandments, a creed, and an ecclesiastical organization. Having made this covenant, Our Lord established Peter the Rock as the first Pope. Joshua invoked the stone in his farewell speech to the Israelites, before his death. According to the Gospel of St. John (Ch. 21), one of Our Lord’s last acts before His Ascension was to confirm St. Peter in his unique ministry.
Peter is the rock on which Christ built His Church. But Peter and his successors are also infallible (when they exercise their Petrine authority) witnesses, many of them literal martyrs, to the Faith. In this respect, the Papacy (=the Rock of Peter) is like the stone that Joshua invoked as his testimony (martyrion in the Septuagint) against the Israelites should they stray from the covenant. The stone foreshadows the role that the Popes have played in testifying to the True Faith against heretics and schismatics and other covenant-breakers.
Joshua’s “stone” vs. the “Rock” of Peter
You might be wondering about how the “stone” in Joshua compares to the “Rock” in the Gospels. In the Septuagint, Joshua’s stone is a “lithos” (Joshua 24:26-27). The Gospel’s “Rock” is a “petra” (Matt. 16:18). I think it’s fair to see “lithos” and “petra” as belonging to the same semantic range; they mean approximately the same thing and can be used interchangeably. To demonstrate this, I cite St. Peter himself, punning on his name and office as Rock at I Peter 2:1-10 (emphasis added, with another pun highlighted to prove the point):
“ Wherefore laying away all malice, and all guile, and dissimulations, and envies, and all detractions,  As newborn babes, desire the rational milk without guile, that thereby you may grow unto salvation:  If so be you have tasted that the Lord is sweet [chrēstos, “propitious,” but punning on “Christos,” Christ].  Unto whom coming, as to a living stone [lithon], rejected indeed by men, but chosen and made honourable by God:  Be you also as living stones [lithoi] built up, a spiritual house, a holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus [=Joshua] Christ.
 Wherefore it is said in the scripture: Behold, I lay in Sion a chief corner stone [lithon], elect, precious. And he that shall believe in him, shall not be confounded.  To you therefore that believe, he is honour: but to them that believe not, the stone [lithos] which the builders rejected, the same is made the head of the corner:  And a stone [lithos] of stumbling, and a rock [petra] of scandal, to them who stumble at the word, neither do believe, whereunto also they are set.  But you are a chosen generation, a kingly priesthood, a holy nation, a purchased people: that you may declare his virtues, who hath called you out of darkness into his marvellous light:  Who in time past were not a people: but are now the people of God. Who had not obtained mercy; but now have obtained mercy.”
You can find the Greek here. The juxtaposition of lithos and petra at 2:8 shows the semantic proximity of the two words; they mean about the same thing. So there’s no philological obstacle to interpreting Joshua’s lithos as a type of Jesus’ petra, St. Peter.
To be continued . . .
*I prefer the old-timey Papist rendering “Josue,” but I’ll cave to convention. I want people to be able to find this site when they Google “Joshua.”