This paper formulates a stochastic optimal stopping model for the investment of mainframe computers in the telecommunications industry. It describes the investment behavior by focusing on unique features of computers, which are associated with technological development. The optimal investment rule is the solution of a stochastic DP model that specifies the system administrator's objective to maximize profits through the main choices: `keep', `upgrade', or `replace'. If replace, there are various capacity choices. Using a detailed data on computer holdings by one of the largest telecommunication companies, I investigate the explanatory facts of computer replacement and estimate the model with the NLS-NFXP algorithm. The estimation and simulations of the estimated model support the observed explanatory facts of the data and predict the data well enough to assure that the firm follows an optimal investment strategy to replace and upgrade its computer.