Abstract: Among numerous tertiary technologies, Alkaline-Surfactant-Polymer(ASP) flooding is one of the most important enhanced oil recovery methods. In this method, the ASP solution system exhibits the characteristics of a non-Newtonian power-law fluid. A homogeneous well test model based on non-Newtonian power-law fluid is nonlinear and it is very difficult to obtain explicit exact analytical solutions. Generally, one can only obtain approximate solutions with numerical methods. Recently, an advanced method of separating variables with additions was proposed by the authors, which can be used to obtain exact analytical solutions . This method in this paper is used to solve the unsteady nonlinear well test equation. A series of exact analytical solutions(without using special functions or infinite series) are derived based on the theory of non-Newtonian power-law fluid. They can be used as the benchmark solutions to check the accuracy, convergence and stability of the numerical solutions and to develop the numerical computational approaches.