The present work consists of a theoretical investigation of the shear response of a truncated two-dimensional elastic wedge subject to an arbitrary disturbance. Expressions are derived for the deflections and shears which develop in the wedge owing to an imposed time-dependent disturbance. The frequencies of the wedge are derived for the six first modes of oscillation and are given graphically for different degrees of truncation for the one and two-dimensional cases. The solution derived is applicable to earthquake engineering problems, in particular to those dealing with the seismic stability of earth dams and embankments. The concept of strong ground-motion spectra is introduced and its advantages and limitations are discussed briefly.