Surface and interfacial impedance matrices play an important role in the construction of Green's functions, the analysis of surface and interfacial waves and the stability assessment of pre-stressed half-spaces or joined half-spaces. This paper studies these matrices for generally anisotropic pre-stressed incompressible elastic materials. It is shown that the surface-impedance matrix satisfies a simple matrix equation which, for plane-strain deformations, can be solved exactly. As a result, explicit secular equations for surface and interfacial wave speeds and explicit wrinkling/buckling conditions for pre-stressed half-spaces and joined half-spaces are obtained. It is also shown that the plane-strain surface-wave problem is mathematically identical to the edge-wave problem for thin elastic plates. Thus, the uniqueness of surface-wave speed is settled by drawing upon a recent proof of the uniqueness of edge-wave speed. Examples are used to show that it is straightforward to solve the secular equations based on the given formulae either exactly (where possible) or numerically.