In this paper two problems will be solved analytically: the reflection of plane stress waves at a free boundary and the reflection and refraction of plane stress waves at a welded interface separating two dissimilar materials. In particular, stress reflection and refraction coefficients will be derived and the superimposed state of stress in regions of wave interference will be calculated. The solutions are visualized in a series of examples by means of computer-generated isochromatic fringe patterns. They show the partition of stress between reflected and refracted waves, stress distribution in regions of wave interference and demonstrate stress wave propagation in laycred structures.