A numerical study of water-wave refraction problems is performed. The analysis is based on the linear wave theory and the parabolic approximation, which provides the forward scattered wave field. Two problems are considered in particular: (1) the diffraction of monochromatic waves by a thin breakwater in a slowly varying depth and (2) the wave field near caustics predicted by linear wave ray theory. Numerical solutions of these problems are compared to either analytical results or laboratory experimental data.