In this paper, we examine set-valued mappings with weakly convex graphs and provide sufficient conditions for their Lipschitz properties. Michael’s theorem is a fundamental result on the existence of continuous selections for lower semi-continuous mappings with closed convex images. In this paper, we present a refinement of Michael’s theorem for set-valued mappings with convex graphs and weakly convex graphs. In addition, the problem of the existence of directionally-differentiable selections is discussed.