This contribution presents new algorithms for the automatic simplified computation of symbolic transfer functions of linear circuits. The problem of symbolic simplification of transfer functions is defined and a set of algorithms able to cope with this problem and the simplified computation of poles and zeroes is developed and discussed. Results are reported with examples of circuits analyzed by our algorithms, showing good accuracy in their approximation, when compared to the corresponding SPICE simulations. Our technique merges the simplification procedure and the evaluation of the transfer functions, thus achieving significant improvements in terms of CPU time, compared with direct evaluation of the functions themselves.