This paper presents an overview of constitutive modelling of unsaturated soils and the numerical algorithms for solving the associated boundary value problems. It first discusses alternative stress and strain variables that can be used in constitutive models for unsaturated soils. The paper then discusses the key issues in unsaturated soil modelling and how these issues can be incorporated into an existing model for saturated soils. These key issues include (1) volumetric behaviour associated with saturation or suction changes; (2) strength behaviour associated with saturation and suction changes, and (3) hydraulic behaviour associated with saturation or suction changes. The paper also shows how hysteresis in soil–water characteristics can be incorporated into the elasto-plastic framework, leading to coupled hydro-mechanical models. Finally, the paper demonstrates the derivation of the incremental stress–strain relations for unsaturated soils and discusses briefly the new challenges in implementing these relations into the finite element method.