Successful biological development via spatial and temporal regulations of cell differentiation relies on the action of multiple signaling molecules that are known as morphogens. It is now well established that biological signaling molecules create nonuniform concentration profiles, called morphogen gradients, that activate different genes, leading to patterning in the developing organisms. The current view of the formation of morphogen gradients is that it is a result of complex reaction diffusion processes that include production, diffusion, and degradation of signaling molecules. Recent studies also suggest that the degradation of morphogens is a critically important step in the whole process. We develop a theoretical model that allows us to investigate the role of a spatially varying degradation in the formation of morphogen gradients. Our analysis shows that the spatial inhomogeneities in degradation might strongly influence the dynamics of formation of signaling profiles. Physical chemical mechanisms of the underlying processes are discussed.