Instead of the &&functional'' mode shapes (de"ned by the admissible, comparison or eigenfunctions) employed by the classical assumed mode (or modal analysis) method, the lowest several &&numerical'' (or vector) mode shapes and the associated natural frequencies of a &&non-periodic'' multispan pipe with the prescribed supporting conditions and "lled with the &&stationary'' #uid (with velocity ;"0) are determined by means of the transfer matrix method (TMM). Using the last mode shapes together with the natural frequencies and incorporating with the expansion theorem, the partial di!erential equation of motion for the in"nite degree-of-freedom (d.o.f.) continuous multispan pipe "lled with &&#owing'' #uid (with ;O0) is converted into a matrix equation. Solving the last matrix equation with the direct integration method gives the dynamic responses of the #uid-conveying pipe. Since the order of the transfer matrix for either each pipe segment or the entire piping system is 4;4, which is independent of the number of the spans for the system, the presented approach is simpler than the existing techniques, particularly for the piping systems with large number of spans. It is also noted that the classical assumed mode (or modal analysis) method is easily applicable only to the special cases where the functions for the approximate mode shapes are obtainable, such as the &&single-span'' beams or the &&periodical'' multispan beams (with identical spans and identical constraints). However, the presented &&numerical'' (or vector) mode method is suitable for many practical engineering problems.