Abstract: A new algorithm SSTMSD for finding symbolic determinants——state space tree method for determinants is presented by applying LIFO branch-and-bound search technique and the concept of state space tree (it is the development and improvement of Minty algorithm). Based on it and by applying the concept of modified graphs, a new algorithm SSTMSF for finding symbolic system functions-state space tree method for system functions is proposed. As compared with the current conventional methods (e. g. signal flow graph method and directed tree method, etc.), SSTMSF has the following two advantages:(1) Its computing efficiency is higher and its resulted expressions are shorter. (2) The denominator (determinant) and numerator (cofactor) of a symbolic system function can be separately found by repeatedly call the same one procedure SSTMSD.