The deformational response of plastic board drains installed to accelerate consolidation of soft soils, is examined as a problem of downdrag. The drain is modelled as a beam-column in which the axial load increases nonlinearly with depth. The soil response is represented by the Winkler medium whose coefficient of subgrade modulus increases linearly with depth. The governing equations for the drain-soil system are derived and solved as an eigenvalue problem. The critical buckling loads and the shape of the drain are obtained as functions of the normalized subgrade modulus of the soil at the top, the parameters signifying the variation of axial load along the length of the drain and the increase of subgrade modulus with depth. The derived deformed shapes of the drain are consistent with the observed ones.