The Raman G and 2D bands of uniaxially strained graphene are studied within a non-orthogonal tight-binding model for parallel scattering geometry and laser photon energy of 2.5 eV. The derived strain rate of the G band, as well as its intensity as a function of the strain direction and light polarization angle, are found in very good agreement with previous reports. The simulated 2D band shows a complex peak structure with two or three resolved subbands. The dependence of the strain rate and the Raman intensity of the latter on the strain direction and light polarization angle follows simple trigonometric expressions. Noticeable deviations from these expressions are observed for the polarization angle dependence. It is also shown quantitatively that the contribution to the 2D band of the "inner" processes is about 10 times larger than that of the "outer" processes. Our predictions for the 2D band behavior of strained graphene can be used for monitoring the strain in graphene-based applications by Raman spectroscopy.