A common task in computer graphics is the visualisation of models of real world objects. These models are very large and complex and their surfaces are usually represented by triangular meshes. The surface of complex model can contain thousands or even million of triangles. Because we want fast and interactive manipulation with these models, we need either to improve our graphics hardware or to find a method how to reduce the number of triangles in the mesh, e.g. mesh simplification. In this paper we will present a fast algorithm for triangular mesh reduction based on the principle of vertex decimation.