Pensions are an essential component of society, and owing to rising population aging, life expectancy, healthy living years, and a lower fertility rate, financial sustainability will be a worldwide issue in the future. The purpose of this chapter is to examine the influence of social and economic variables on pensions and financial sustainability, as well as to suggest some methods to enhance the well-being of the elderly Romanian population using technological modeling. The R square indicates that 99.47% of the development of variable pension (Y) is described by the evolution of social variables (X1-X7) and 99.98% is explained by the evolution of economic factors (X8-X14) using mathematical modeling. The correlations between variables and covariance indicate an effect on the pension fund's stability and financial sustainability. The professionals might use technological modeling to develop future sustainable solutions for the pension system and to enhance the well-being of the elderly Romanian pension population.