A layer-by-layer method of stress calculation in symmetrical pairs of layers is proposed to estimate the bearing capacity of composite pressure vessels, for which simple criteria of biaxial tensile strength of composite pipes are substantiated. According to the model of a diamond-shaped (rhombus) assembly of inextensible fibers, the limiting surface in the stress space represents a rectangle. Stresses corresponding to the points on the sides of this rectangle determine the conditions of different types of failure: matrix cracking or fiber bursting. The limiting surface can be described by a single equation of an inclined ellipse. We propose a simple method for constructing the limiting surface for a pair of symmetrically wound layers based on only two values of winding strength (0) and (+45°) under uniaxial axial tension. Comparison of the calculated stresses with the ultimate surface for each pair of layers allows one to formulate the optimal design problem in terms of equality of safety factors for each pair of layers.