We present an algorithmic procedure for the nite element solution of structural problems for no-tension materials. The approach is based upon a suitable modi cation of the tangent strategy which is shown to be computationally superior to conventional procedures for non-linear material models, namely the tangent strat- egy enhanced with line searches and the tangent-secant approach. The solution of the constitutive problem for no-tension materials is derived by an original path of reasoning and its formulation in a strain-driven format, directly amenable to a computer implementation, is presented. For completeness the existing expressions of the tangent and secant operators for the no-tension model are brie y recalled and an original formula for the secant operator derived. The robustness of the proposed strategy is exempli ed by the numerical results obtained for a masonry panel with openings. Remarkably, the solution is achieved by assigning a single load step and an asymptotically quadratic convergence rate is attained. Further, the numerical properties of the proposed solution strategy are practically una ected by the adopted discretization.