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Conventional constitutive models developed for saturated soils are inadequate when analysing problems involving unsaturated conditions. Although unsaturated constitutive models are available in the Imperial College Finite Element Program (ICFEP), there are aspects of unsaturated soil response that are not adequately simulated. The aim of the present thesis is to develop and implement numerical expressions describing the most relevant of these features and to apply them in combination with the existing ICFEP capabilities to boundary value problems involving unsaturated soils. The over-prediction of the peak shear stress exhibited by overconsolidated soils and the simplicity of the soil-water retention relationship employed, constitute the focal points of the improvements suggested. A new surface is introduced to substitute for the yield and plastic potential functions on the dry side of critical state, in order to prevent the available constitutive models from overestimating the peak deviatoric stress. The development, implementation and calibration of this surface are presented, followed by analyses of laboratory experiments demonstrating the improved simulation of soil behaviour. Novel formulations are proposed for the soil-water retention curve, which defines the relationship between the degree of saturation or the water content and the applied suction, modelling its hysteretic nature and incorporating the effect of specific volume. Ultimately, a three-dimensional hysteretic surface, defined in terms of degree of saturation, suction and specific volume, is presented. The new developments are subsequently applied to the numerical analysis of boundary value problems involving (a) the stability of slopes in overconsolidated unsaturated soils and (b) the behaviour of unsaturated soil slopes under seasonal changes of suction, highlighting the importance of adopting appropriate constitutive models.