This paper proposes an algorithm for performing explicit integration of constitutive models for unsaturated soils in problems where consideration of stress rate objectivity becomes necessary due to large deformations. As many constitutive models for unsaturated soils incorporate suction forces, as well as stresses and strains, into the material description, an accurate integration procedure is more complicated than similar schemes proposed for saturated soils. The difficulties of integration are also coupled with the need to incorporate objectivity (frame independency) within the integration procedure. Application of the proposed method is limited to constitutive models that assume additive decomposition of the strains. A fully coupled finite deformation numerical model is considered with displacement, pore water pressure and suction as the nodal variables. Details of the implementation of the stress integration algorithm at each stage of an analysis are given. The algorithm is then applied to solve some large-scale geotechnical problems. Numerical examples are also provided to assess the performance of the algorithm under different loading conditions.