The problem of the coseismic deformation of an earth model consisting of an elastic layer of uniform thickness overlying an elastic half-space due to a very long tensile fault in the layer is solved analytically. Integral expressions for the surface displacements are obtained for a vertical tensile fault and a horizontal tensile fault. The integrals involved are evaluated approximately by using Sneddon’s method of replacing the integrand by a finite sum of exponential terms. Detailed numerical results showing the variation of the displacements with epicentral distance for various source locations in the layer are presented graphically. The displacement field in the layered half-space is compared with the corresponding field in a uniform half-space to demonstrate the effect of the internal boundary. Relaxed rigidity method is used for computing the postseismic deformation of an earth model consisting of an elastic layer of uniform thickness overlying a viscoelastic half-space.