An SL(2, Z) family of string solutions of type IIB supergravity in ten dimensions is constructed. The solutions are labeled by a pair of relatively prime integers, which characterize charges of the three-form field strengths. The string tensions depend on these charges in an SL(2, Z) covariant way. Compactifying on a circle and identifying with eleven-dimensional supergravity compactified on a torus implies that the modulus of the IIB theory should be equated to the modular parameter of the torus.