A truss topology optimization problem under stress constraints is formulated as a mixed integer programming problem with variables indicating existence of nodes and members. The local constrains on nodal stability and intersection of members are considered, and a moderately large lower bound is given for the cross-sectional area of an existing member. A branch-and-bound method is presented for obtaining good lower-and upper-bound solutions. A method is also presented for obtaining an approximate solution by successively solving relaxed nonlinear programming problems based on a variable fixing technique.