We present analytical solutions for density profiles of homopolymer melts and of the mathematically equivalent, incompressible polymer solutions near heterogenous, periodically patterned surfaces. The theory employs an analytic density functional-self-consistent field theory, and particular applications consider striped and checkerboard patterns. The computations illustrate the competing influences of the pattern size and the bulk correlation length xi on the density profile both at the surface and orthogonal to the surface. The density profiles are determined by the bulk correlation length xi if the thickness of the stripes L is larger than 2 xi and by L if L < 2 xi. (C) 2000 American Institute of Physics. [S0021-9606(00)51713-9].