We modify the Modified Cam-Clay (MCC) model for large stress ranges encountered in geological applications. The MCC model assumes that the friction angle and the slope of the compression curve of a mudrock are constant and thus predicts constant values for the lateral effective stress ratio under uniaxial strain (K0) and the undrained strength ratio. Experimental work, however, show that these properties vary significantly with stress over large stress ranges (up to 100 MPa). We incorporate the stress dependency of the friction angle and the slope of the compression curve into the MCC model. The modified model, with only one additional parameter, successfully predicts the stress dependency of the stress (K0) and strength ratios. We encode the modified model and use it in the finite-element analysis of a salt basin in the deepwater Gulf of Mexico. The new model predicts that the stress field around salt is significantly different than predicted by the original MCC model. We also illustrate that the stress dependency of the friction angle has significant consequences for drilling and geological processes: it causes 1) a concave profile for the topography and convex profile for thrust faults in critical wedges with planar decollement; 2) higher magnitudes and narrower range for appropriate mud weights for drilling a wellbore; and 3) deep-seated failure of submarine channel levees at a lower angle. Our study could improve in situ stress and pore pressure estimation, wellbore drilling, and quantitative understanding of geological processes.