In this paper we study the directions of periodicity of multidimen-sional subshifts of finite type (SFTs) and of multidimensional effectively closed and sofic subshifts. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope representing that direction. In this paper, we prove that Σ 0 1 sets of non-commensurable Z 2 vectors are exactly the sets of slopes of 2D SFTs and that Σ 0 2 sets of non-commensurable vectors are exactly the sets of slopes of 3D SFTs, and exactly the sets of slopes of 2D and 3D sofic and effectively closed subshifts.