In this paper, we present a framework for the groupwise processing of a set of meshes in dense correspondence. Such sets arise when modeling 3D shape variation or tracking surface motion over time. We extend a number of mesh processing tools to operate in a groupwise manner. Specifically, we present a geodesic-based surface flattening and spectral clustering algorithm which estimates a single class-optimal flattening. We also show how to modify an iterative edge collapse algorithm to perform groupwise simplification while retaining the correspondence of the data. Finally, we show how to compute class-optimal texture coordinates for the simplified meshes. We present alternative algorithms for topologically symmetric data which yield a symmetric flattening and low-resolution mesh topology. We present flattening, simplification, and texture mapping results on three different data sets and show that our approach allows the construction of low-resolution 3D morphable models.