Large installation of distributed generations (DGs) of renewable energy sources (RESs) on distribution network has been one of the challenging tasks in the last decade. According to the installation strategy of Japan, long-term visions for high penetration of RESs have been announced. However, specific installation plans have not been discussed and determined. In this paper, for supporting the decision-making of the investors, a new scenario-based two-stage stochastic programming problem for long-term allocation of DGs is proposed. This problem minimizes the total system cost under the power system constraints in consideration of incentives to promote DG installation. At the first stage, before realizations (scenarios) of the random variables are known, DGs’ investment variables are determined. At the second stage, after scenarios become known, operation and maintenance variables that depend on scenarios are solved. Furthermore, a new scenario generation procedure with clustering algorithm is developed. This method generates many scenarios by using historical data. The uncertainties of demand, wind power, and photovoltaic (PV) are represented as scenarios, which are used in the stochastic problem. The proposed model is tested on a 34 bus radial distribution network. The results provide the optimal long-term investment of DGs and substantiate the effectiveness of DGs.