This is a great question. There are many reasons why Abraham is considered a model of faith. Let me list three of them.
First, in Genesis 12, God tells Abram to leave his people and all that he knows to a foreign land. What does he do? He actually listens to God and trusts in his promises of blessings and goes. (Genesis 12:1-4) It is important to keep in mind that Abram does not really know where he is going.
Second, God promises to give him a son from his wife, Sarah. However, there is one problem. Sarah is much too old to have children. The text makes this point view clear in Genesis 15:1-6. Romans 4 in the New Testament is even stronger in it language, as Paul speaks of the "deadness" of Sarah's womb. It is clear from Genesis 15:6 that Abram believes that God can give him a son through Sarah and for this reason God calls him righteous. Later Abram's name is changed to Abraham (Genesis 17)
Third, after God gives Abraham a son, Isaac, God now tells him to offer his only son to him as a sacrifice. Abraham does the unthinkable; he is willing to offer his son to God in Genesis 22. God sees this and stops the sacrifice and calls Abraham a man of faith.
Abraham, one of the three patriarchs of Judaism, is regarded as a model of faith because he is called on to sacrifice his beloved son, Isaac, and does so, following God's commandment. Abraham waits a long time to have a son with his wife, Sarah, and is 100 when Isaac is born. When Isaac is a child, as told in Genesis 22, God commands Abraham to bring Isaac to a remote mountain and sacrifice him. Along the way, Isaac asks Abraham where the offering is that they are bringing to God, and Abraham answers that God will provide a lamb.
Right before Abraham is going to sacrifice his beloved son, the angel of God makes a ram whose antlers are caught in a thicket appear. Abraham is able to sacrifice this ram instead of Isaac, and his son is saved. Abraham does as God commands, and he has constant faith in God. He believes that even if God allows him to sacrifice Isaac, God will raise Isaac from the dead. Abraham's faith in God never wavers.