A general approach is presented for risk engineering and identification of the risk benefits analysis, goals and limits for risk evaluation in certain applications by considering the first-degree secondary moment methods. A computer program is developed in the Java language (DAM_RISK) with the aim to determine the safety levels of spillways in existing dams (or dams in the planning or construction phase). In consideration of a possible risk, observed overflow values are used, with the purpose of the rehabilitation values that need to be known, thus producing data ready for technical and financial analysis. This program is used to perform risk analysis for the Kurtun and Oymapinar dams in Turkey with the purpose dam rehabilitation at risk. Different spillway dimension and the change in risk for the reservoir damping factors are also presented. The most important conclusion for planners and risk evaluators is the graph that shows the riskless region in spillway dimensions. Various features of the computer program and areas in which it might be further developed are considered in detail. The results of the applications carried out are given in terms of risk evaluations.