Diffusion of a point-like particle in a thin layer of varying thickness h(x, y) bounded by reflecting boundaries is considered. Using the mapping technique derived for diffusion in a non homogeneous quasi-1D channel, we derive an effective two-dimensional Fick-Jacobs (FJ) equation governing evolution of the marginal density p(x, y, t) of the planar coordinates x and y. The equation is modified by the space-dependent effective diffusion coefficient D(x, y), which is a 2x2 tensor introducing anisotropy of diffusion, depending on the shaping function h(x, y). Biasing of the diffusional flux is demonstrated on a layer bounded by the sinusoidally corrugated upper wall.