A new algorithm for the optimal stope design problem is proposed. It is based on a previous methodology developed by Bai et al. (Comput Geosci 52:361-371, 2013a) where a cylindrical coordinate system is used to define geomechanical restrictions and to find the optimal stope around an initial raise. The new algorithm extends this work using an integer programming formulation and a new set of constraints, aimed to solve geomechanical issues present on the original methodology. The new formulation is tested on two synthetic and one real deposits. An economic, geomechanical and feasibility analysis is performed, comparing the new results with Bai's methodology. This methodology achieves better stope designs in terms of geomechanical stability and wall regularity, generating feasible stopes for real use. It also allows further extensions to incorporate other geometrical constraints in order to obtain more regular stope designs.