To treat cancer, knowledge of mechanical parameters can be essential. This study proposes a new approach for estimating hydraulic conductivity (k) and hydraulic conductivity ratio (α) of a living tissue, based on inverse methods, allowing tissue parameter estimation using only a limited set of measurements. First, two population-based algorithms (Levenberg-Marquardt (LM) method and conjugate gradient (CG) method) and two gradient-based algorithms (genetic algorithm (GA) and particle swarm optimization (PSO) algorithm) are considered, and a comparative study between these different inverse methods is performed to determine which methods have a good performance in terms of convergence rate and stability. CG method is shown to perform well in the case of noise-free input data; however, in the case of noisy input data, it fails to converge. The other three methods (LM, GA, and PSO) converge with estimation errors <10% in both noise-free and noisy input data, suggesting their utility to tackle this problem. In the second part, the effectiveness and good accuracy of these robust algorithms (LM, GA, and PSO) are validated with experimental results. The hydraulic conductivity and hydraulic conductivity ratio of a specific living tumor tissue are then estimated for mammary adenocarcinoma (R3230AC). Moreover, assuming measurement of only one-point interstitial pressure inside the tumor, the effect of the location of this one-point on estimation accuracy of hydraulic conductivity is investigated. We show that estimation errors for points measured near the surface and center of the tumor are greater than at other points.