A method is proposed for constructing exact solutions to boundary value problems of the theory of elasticity in a rectangle with stiffeners located inside the region (an inhomogeneous problem). The solutions are represented by series in Papkovich–Fadle eigenfunctions, the coefficients of which are determined explicitly. The method is based on the Papkovich orthogonality relation and the theory of expansions in Papkovich–Fadle eigenfunctions developed by the authors in homogeneous boundary value problems of the theory of elasticity in a rectangle (the biharmonic problem). The solution sequence is demonstrated with the example of an even-symmetric problem for a rectangle the sides of which are free, and an external load acts along the stiffener located on the axis of symmetry of the rectangle.