Is Luke’s sermon here (Luke 6:17-49) the same occasion as Matthew’s Sermon on the Mount (Matthew 5:1-7:29)? The appointment of the apostles obviously could not come before the call of Matthew to be a disciple. Matthew places his own call (Matthew 9:9-13) after the Sermon on the Mount, but Luke places the call of Matthew (also known as Levi) before his sermon (Luke 5:27-32). That might seem to indicate that Luke's very similar sermon was delivered on a different occasion, but we cannot be sure because Matthew often rearranges material in his Gospel.
The different circumstances between Mathhew's and Luke's sermons might suggest they are not the same: Jesus standing in Luke and sitting in Matthew, a plain in Luke and a mountain in Matthew, healing taking place in Luke and no healing mentioned in Matthew. The reference to a plain in Luke and a mountain in Matthew may result from his preceding his sermon with Christ praying and the appointment of the twelve, which took place higher up the mountain. (Matthew again moves the appointment of the twelve elsewhere in his Gospel, and places it alongside the sending out of the twelve to preach (Matthew 10)). From Luke’s perspective they came down to the plain. If the plain was also up in the mountain, then from Matthew’s perspective, they went up the mountain. As far as the other differences are concerned, the Lord may have sat initially and then stood to teach – it was a great multitude he was speaking to. The reference to healing in Luke and not in Matthew is not conclusive; it is often the case that one Gospel writer includes details that another leaves out, even though they are describing the same event. The preludes to the two sermons are also similar, recording people coming from far away from the same regions. But this need only indicate that these two sermons were close together though not necessarily the same occasion.
What follows these two sermons is also similar. Luke records the healing of the centurion's servant after his sermon and Matthew does the same, both Gospels commenting that Christ entered into Capernaum at that time. Matthew however inserts the account of the healing of the leper between the end of the sermon and the healing of the centurion’s servant, and he has a strong time signature for this (Matthew 8:1). Luke has the healing of the leper back in chapter 5:12-16, and Matthew is a little vague about the time of entering into Capernaum (Matthew 8:5).
There are also differences in the content of the two sermons. These may be more conclusive. Luke’s sermon is considerably shorter. Luke presents the material in a different order and has content not found in Matthew, and some things that are said in Luke are said differently. Hendriksen (Matthew p 260) understands Matthew's and Luke's sermon to be the same, but others are persuaded that the differences are significant enough to point to two different sermons. The similarity in content is easily accounted for. We know that Christ said the same things on different occasions – this is certain because a single Gospel writer sometimes has the same saying in two places (e.g. Matthew 10:39; 16:25). Every good teacher repeats himself for emphasis and for instruction. Different people were present in different locations and needed to hear the same teaching. So we will treat these as two different sermons.