Value at Risk (VaR) is one of the widely employed risk measures in quantitative risk management. Because of its readiness of use, both theoretical and practical researches have been extensively made so far. Here, in this paper, we are concerned with the estimation of VaR for the portfolio problem; the portfolio consists of two random variables. Our innovative point is that we do not necessarily assume the independence between random variables but the possibility of nonlinear relation. To analyze the nonlinear dependence, a copula function method is customarily used; as is well-known, copula provides a flexible tool for treating the possible nonlinear relation. We derive the determination formula of VaR analytically in the case of Archimedean copulas, which may be served as elementary machinery of computation. Empirical studies are also implemented for the problem of estimating VaR in stock indexes. The results show that our obtained formula works rather well.