A simple formulation applicable to topology modification is presented for exact reanalysis of static response of trusses based on general methods of inverting modified matrices. A random search algorithm is also presented for topology optimization of trusses with discrete list of cross-sectional areas. It is shown that the exact reanalysis is very effective for the case where the cross-sectional area of only one member is modified at each step for generating a neighboring solution. The difficulty due to discontinuity in the stress constraints is successfully avoided by considering the cross-sectional areas as discrete variables. (C) 2001 Elsevier Science Ltd. All rights reserved.