An elastic analysis is presented to study the working load response of an axially loaded single elastic pile embedded in a linearly non-homogeneous incompressible elastic (Gibson) soil. The analysis ensures compatibility of displacement in the vertical and the radial directions along the true contact surface between the pile and the surrounding soil medium. Comparisons are presented to verify the accuracy of existing solutions based on approximate analysis methods. Selected numerical results are presented to portray the influence of the degree of non-homogeneity of soil on the axial stiffness and load-transfer and contact traction curves of a single elastic pile. -from Author