Abstract
In this work we introduce a new mathematical model for elastic beams with a cross‐section of constant width and longitudinally variable depth, obtained from the classical three‐dimensional linear elasticity problem by using an asymptotic expansion method. We characterize the first‐ and second‐order displacements and the first‐order stress field, giving results related to existence, uniqueness and convergence for the limit model solution. Finally, we present the computations for a classical example.