Abstract This paper presents a new analytical method for an exact solu-tion of the presure transient problems for general radial and linear models with heterogeneities. In these models, the stora-tivity and the transmissivity coefficients are considered functions of the distance from the well. The solution method is based on special transformation of variables which reduces the problem to a diffusivity equation with constant coefficients. This equation is then solved in the Laplace transform domain and the solution is inverted into the real time domain by the Stehfest algorithm. The solution method allows both continuous variation as well as discontinuities of the rock and fluid properties. The new solution algorithm reproduces exactly all known exact solutions for specific variation of properties including the multicomposite radial and linear model solutions.