The Fréchet distance is a measure of similarity between curves or surfaces. The Fréchet distance between two polygons can be computed in polynomial time, but it is much harder to compute the Fréchet distance between surfaces. We present the ﬁrst (1+ε)-approximation algorithm and the ﬁrst exact algorithm for computing the Fréchet distance between two surfaces. Next, we show that computing the Fréchet distance between a surface and a triangle is in PSPACE. Combining the approximation algorithm and the exact algorithm, we present an improved version of (1+ε)-approximation algorithm. Finally, we present a new restricted class of surface, surfaces composed of large triangles, for which the Fréchet distance between them can be computed faster.