A new approach for the solution of truss shape and topology optimization problemsunder local and global stability constraints is proposed.By employing the cross sectional areas ofeach bar and some shape parameters as topology design variables,the difficulty arising from thejumping of buckling length phenomenon can be easily overcome without the necessity of introduc-ing the overlapping bars into the initial ground structure.Therefore computational efforts can besaved for the solution of this kind of problem.By modifying the elements of the stiffness matrixusing Sigmoid function,the continuity of the objective and constraint functions with respect toshape design parameters can be restored to some extent.Some numerical examples demonstratethe effectiveness of the proposed method. A new approach for the solution of truss shape and topology optimization problemsunder local and global stability constraints is proposed.By employing the cross sectional areas ofachbar and some shape parameters as topology design variables, the difficulty arising from thejumping of buckling length phenomenon can be easily overcome without the necessity of introduc-ing the overlapping bars into the initial ground structure. whereforefocalational efforts can besaved for the solution of this kind of problem.By modifying the elements of the stiffness matrix using Sigmoid function, the continuity of the objective and constraint functions with respect toshape design parameters can be restored to some extent.Some numerical examples demonstrate the effectiveness of the proposed method.