This paper presents a matrix formulation and explicit expressions for the first- and second-order stiffness matrix and loading vector of a prismatic pile with generalised rotational and lateral translation end-constraints on homogeneous or non-homogeneous Pasternak soil. The expressions for the load vector account for any external transverse load that fits a quadratic function. The proposed approach can be used to study a variety of soil–structure interaction problems such as (a) beam columns on non-homogeneous soil, (b) piles subjected to external lateral earth pressures, (c) lateral behaviour of piles fully or partially embedded in layered soils, (d) buckling analysis of piles fully or partially embedded in layered soils and (e) second-order effects in piles, among others. The proposed formulation is easy to incorporate into an existing matrix structural analysis code. Two examples are provided to show the simplicity and practicality of the approach.