In this paper, we apply the multi-wave method to find new multi wave solutions for an important nonlinear physical model. This model is well known as generalized form of Benjamin Bona Mahony (BBM) equation. Using the mathematics software Mathematica, we compute the traveling wave solutions. Then, the multi wave solutions including periodic wave solutions, bright soliton solutions and rational function solutions are obtained by the multi wave method. It is seen that this method is very useful mathematical approach for generalized form of BBM equation.