In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman–Oppenheimer–Volkov equations, we explore the relativistic anisotropic Lane–Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behavior of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed.