Abstract Field analyses of Plio-Quaternary compressional deformations in Taiwan have enabled us to reconstruct the paleostress trajectories resulting from the collision of the Luzon arc (Philippine Sea plate) with the Chinese continental margin (Eurasian plate). The direction of the maximum compressional stress σ 1 shows a fan-shaped pattern that we interpret as resulting from the collision of a rigid body (the Luzon arc) indenting a more deformable material (the thick sediments of the Chinese continental margin). Simple analytical models qualitatively explain the fan-shaped pattern, but the influence of various parameters such as boundary conditions and rheology cannot be quantitatively accounted for by this approach. Consequently, we have used a finite element technique to compute the stresses and strains induced by the push of a rigid body against a two-dimensional, viscous material. The boundary conditions are the velocities based on plate kinematics. A motion in the N300°E direction best explains the stress trajectories observed in central Taiwan. Viscosity contrasts as well as small changes in the shape of the northern edge of the indenter have little influence on the computed stress pattern. The most important parameter is the direction of convergence. Our model quantitatively explains the general pattern of the stress trajectories observed in the collision zone of Taiwan, between the Philippine Sea plate and Eurasia.