In this paper the multi-input Sliding Mode control of nonlinear uncertain non-affine systems with mono-directional actuators is considered. The geometric properties of the regular simplices of vectors are exploited by the mono-directional actuation system. The proposed full-state feedback control method introduces integrators in the input channel and suitably modifies the sliding output to be steered to zero. The resulting high frequency gain matrix (HFGM), which is the matrix multiplying the control vector, turns out to be affected by time and state dependent uncertainties. An effective use of the integral Sliding Mode method in connection with a non-conventional simplex based switching logic is introduced. The proposed simplex control procedure is adequately designed to avoid any possible unbounded increment of the control actions despite the presence of integrators in the input channel and the exploitation of mono-directional devices.