St. Matthew’s preference for this phrase is consistent with his emphasis on the heavenly kingdom descending upon earth. In the great Lord’s Prayer, the kingdom comes on earth as it is in heaven. The Kingdom of Heaven serves as an image of the coming reign of Christ. In His earthly ministry, Messiah begins to undo the darkness of the old world by bringing from heaven a kingdom of light. As David Garland puts it:
The kingdom of heaven is favored because it is a way of referring to God’s transcendent work and lordship that is coming down from heaven…it serves as an image for God’s sovereignty as Lord of heaven who will make all things right on earth.
 David Garland, A Literary and Theological Commentary on Matthew, pg. 48.