In the design of microwave multi-stage amplifiers composed of N amplifier modules, the variation of performances of amplifier as various connection length between modules has been studied. In addition, the methods, equations and conditions for the maximum gain or the most flat gain are presented. The results of sensitivity analysis for the connection length showed that the small change in phase of input, output reflection coefficients(S$_{11}$, S$_{22}$) of module itself is the most important in determination of connection length for the most flat gain. Th egain flatness of 2-module amplifier of which connection length between modules had been determined by presented methods was the best one out of performances with various arbitrary connectio lengths.s.