Injection or production of fluids from subsurface reservoirs lead to stress changes affecting both reservoir and surrounding rocks. For low-permeable caprocks overlying such reservoirs, the movement of pore fluids to or from the formation is restricted and the immediate and short-term response to changes in the stress field will be undrained. Consequently, stress changes transfer partly into pore pressure changes. The aim of the current study is to investigate theoretical means of forecasting the undrained pore pressure generation in the Draupne Formation shale and to compare predictions with experimental results. Predictions are based on measurements from a single undrained triaxial test on a sample with known orientation, and a combination of Skempton's classical formulation and anisotropic poroelastic theory. The predicted pore pressures are compared to measured pore pressures from a series of triaxial tests on samples with various orientations exposed to different total stress paths. First, it is confirmed that the normalized undrained pore pressure measured is linearly connected to the total stress path. Then it is demonstrated that a tensorial pore pressure parameter can be used to accurately predict the influence of stress orientation on generated pore pressure. Lastly, it is experimentally confirmed that the two predictions can be combined to predict the pore pressure arising from stress changes along any compressional stress path and orientation. The observations herein may contribute significantly to the understanding of induced pore pressure in low-permeable materials and provide valuable input to geomechanical modeling of various field operations.