Abstract In this study, a theoretical analysis is presented to estimate the in-plane large displacement elastic stability behavior of structures having non-prismatic members of linearly and nonlinearly varying sections resting on elastic foundation (Winkler type) and subjected to static loads applied at joints only. The analysis adopts the beam-column approach and models the structural members as beam-column elements resting on distributed springs. The formulation of beam-column element is based on Euler approach allowing for the influence of the axial force on bending stiffness. Changes in member chord length due to axial deformation and flexural bowing are taken into account. The stability and bowing functions are estimated using methods of finite differences and finite segments. Also, approximate results have been obtained by using approximate stability and bowing functions of linearly and nonlinearly tapered members resting on elastic foundation. A computer program has been coded in QB language to carry out the proposed analysis of structures with prismatic or non-prismatic members of linearly and nonlinearly varying sections resting on elastic foundation. As a result of this study; the only difference between the analysis of non-prismatic members resting on elastic foundation and those which are not, when adopting the beam-column approach, is represented in the stability and bowing functions, and this is reflected directly on the tangent stiffness matrix.