Summary: The axisymmetric deformation of a nonlinearly elastic isotropic compressible infinite elastic body subjected to a concentrated vertical line load is considered. We first derive the solution within the context of the linear theory of elasticity. Then we obtain the governing equations for the nonlinear problem using the principle of stationary potential energy, and use these equations to obtain classes of compressible finite elasticity solutions for the line load problem. Finally, a comparison with finite anti-plane shear of compressible isotropic materials is made.