We propose a technique for simplification and multiresolution modeling of a terrain represented as a TIN. Our goal is to maintain the morphological structure of the terrain in the resulting multiresolution model. To this aim, we extend Morse theory, developed for continuous and differentiable functions, to the case of piecewise linear functions. We decompose a TIN into areas with uniform morphological properties (such as valleys, basins, etc.) separated by a network of critical lines and points. We describe an algorithm to compute the above decomposition and the critical net, and a TIN simplification algorithm that preserves them. On this basis, we build a multiresolution terrain model, which provides a representation of critical features at any level of detail.