SummaryThe first and second boundary value problems of plane elastostatics are solved for the interior of a parabola. A conformal transformation is used to map the interior of the parabola onto an infinite strip. An analytic continuation technique reduces the boundary value problem to the solution of a form of differential‐difference equation. This is solved by a Fourier integral method. The resulting integrals are evaluated by residues to give eigenfunction expansions for the complex potentials.