The boundary element method is used in this paper to calculate the stresses in a finite planar body with a traction free crack present in it. The body is assumed to undergo time-dependent inelastic deformation and is described by an elastic-power law creep constitutive model. A stationary crack is modelled as a very thin ellipse and numerical solutions to the complete transient problem are obtained by step-wise integration in time. The numerical results for stresses near a crack tip are compared with the asymptotic analytical results obtained by other researchers. These asymptotic results are those for a plate with a line crack where the elastic strain rates are neglected relative to the nonelastic strain rates near the crack tips. Both Mode III and Mode I deformation, under time-independent and time-dependent remote loading, are considered in the calculations.