This work studies the effect of mechanically applied uniaxial strain on reverse-bias band-to-band tunneling current in n+/p+ vertical silicon diodes fabricated on {100} and {110} substrate orientations. The Band Structure Lab and nextnano are used to analyze the change in band structure with uniaxial stress applied perpendicular to the tunneling direction along and crystal directions. A theoretical analysis based on the Wentzel-Kramers-Brillouin (WKB) approximation for tunneling probability combined with an uncoupled full-band Poisson equation solver and the calculated band structure changes is developed to model the experimental results. Reasonable agreement between experimental data and theoretical calculations is found when comparing the relative change in tunneling current at 1 V reverse-bias versus strain for different substrate orientation/strain configurations.