The paper deals with a composite element in which the matrix is reinforced with two families of parallel continuous fibres inclined to the x1 axis at the angles n1 and n2. The stress and strain states were determined in an element subjected to normal and tangential loads. The problem of two-criteria optimization is considered. Minimum strain energy and minimum cost of composite element were chosen as criteria. The strain energy is determined with respect to the system of principal axes of stress. Three independent variables: the angle directing the first family of fibres, the angle between two families and volume fraction of fibres are selected as the design variables. Examining particular load cases in composites made with epoxy resin reinforced with carbon fibres elements and in high performance fibre reinforced cementitious composite elements, optimum solutions have been determined in the sense of assumed criteria.