A mathematical model for the determination of micromechanical stress and strain distribution in a unidirectional fibre reinforced composite is developed. The model consists of three phases represented as concentric cylinders, including the existence of an interphase. Both fibre and matrix have well defined elastic properties, while the interphase properties follow an exponential law of variation. The effect of an, abrupt variation of elastic properties at the fibre-interphase boundary on the micromechanical state of stress is also presented. The degree of adhesion between fibre and matrix is described by means of adhesion parameters introduced, and a parametric study is performed wherein the stress and strain distribution around the fibre are determined as a function of adhesion efficiency and fibre volume fraction. Analytical results were confirmed by means of a finite element technique introduced and applied to the model.