We explored and specialized new Lie infinitesimals for the (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii (BKP) using the commutation product, which results a system of nonlinear ODEs manually solved. Through two stages of Lie symmetry reduction, (3 + 1)‐dimensional BKP equation is reduced to nonsolvable nonlinear ODEs using various combinations of optimal Lie vectors. Using the integration and Riccati equation methods, we investigate new analytical solutions for these ODEs. Back substituting to the original variables generates new solutions for BKP. Some selected solutions illustrated through three‐dimensional plots.