In this study, the effect of uniform strain on the tunneling of Dirac fermions in monolayer graphene in the presence of electrostatic potential barriers was investigated. For the calculations, an effective Dirac Hamiltonian including a mass term was employed, and single and double rectangular barriers were modeled under the following assumptions: strain was applied uniformly along both the zigzag and armchair directions; single and double potential barriers were considered; and fermions were assumed to impinge on the obstacles with arbitrary energies and angles. The transmission probability for massive and massless fermions was then calculated using the continuity conditions of the wave function. The results showed that for massless fermions, under normal incidence, perfect transmission corresponding to the Klein tunneling effect was preserved, independent of the barrier height. In the presence of a mass term, an energy region emerged where the transmission probability was significantly reduced. Moreover, the application of strain induced notable quantitative changes, including velocity anisotropy. In general, applying strain along the zigzag direction increases the electron transmission probability compared to the armchair configuration.