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This paper presents the analysis of a distribution system connected with distributed generation (DG) units. The developed technique is based on the steady state voltage stability index. The weakest branches in the distribution system which are more likely go to the instability region are selected for DG allocation. Two optimization methods are utilized to find out the size of the DG corresponding to minimum losses or minimum stability index. The Newton-Raphson load-flow is used to find the steady-state solution of the studied distribution system. The AMPL software package is utilized for evaluating the size of the DG units. The developed methods are tested using a 90-bus distribution system with a variety of case studies.