8 páginas, 8 figuras, 1 tabla., Modal selection induced by parallel polarized optical injection in a vertical-cavity surface-emitting laser (VCSEL) emitting in two transverse modes is analyzed from a theoretical point of view. We show that the selection of the fundamental transverse mode can be achieved when the two transverse modes have parallel polarizations. This selection is accompanied by locking of the fundamental mode to the optically injected signal for large enough values of the wavelength detuning between the fundamental mode and the externally injected signal. The injected power needed to induce modal selection grows as the VCSEL bias current is increased for small positive wavelength detunings, while it is independent on the bias current for larger wavelength detunings. That power exhibits a minimum with respect to the injection wavelength at a value λmin that is slightly longer than the wavelength of the fundamental mode of the solitary VCSEL. We also show that the selection process exhibits bistable behavior when the wavelength of the optically injected signal increases beyond λmin . The width of the bistable region increases linearly with the wavelength of the optically injected signal. Our results show that λmin also increases linearly with the VCSEL bias current. Higher order transverse mode selection and bistability, similar to those found for the fundamental mode, are obtained when the optical injection wavelength is close to that of the higher order mode. Our results are in agreement with the experimental results reported earlier., This work was supported in part by the Ministerio de Educación y Ciencia, Spain, under Project TEC2009-14581-C05-02. The work of M. S. Torre was supported in part by the Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina, under Grant PIP 114-200801-00163.