a b s t r a c tThe multiple Exp-function method is used to construct multiple wave solutions to the (3 + 1)-dimensional generalized BKP equation. The resulting solutions involve generic phase shifts and wave frequencies containing some existing choices. By taking the standard truncated Painlevé analysis, we obtained an auto-Bäcklund transformation and some types of exact solutions of the (3 + 1)-dimensional generalized BKP equation. Moreover, the linear superposition principles of hyperbolic and trigonometric function solutions are also presented.