Abstarct: Displacement back analysis is commonly used in establishing geomechanical parameters in rock mechanics and engineering. There are mainly three types of displacement back analysis methods: inverse solving method, atlas method and direct (i.e. optimal) method. Because of the special advantages, the optimal methods are more and more extensively employed in solving engineering problems. For example, Levenber–Marquardt method, Gauss–Newton method, Bayesian method, Powell method, Rosenbork method, and genetic algorithm have been proposed to obtain optimal values of parameters from measured displacement data. Neural network and genetic algorithm were applied to geotechnical engineering back analysis. However, there are still two problems associated with the optimal method unresolved completely. One is that the relation between the displacement and the mechanical parameters is highly non-linear and complex. Another is that the search for the estimated parameter values is in a large space and is highly multi-modal. In this research, three fuzzy systems used for representing the relation between the displacement and the particle swarm optimization, the imperialistic competitive algorithm and the gradient descent training used for tuning this three fuzzy systems. The particle swarm optimization and the imperialistic competitive algorithm used for searching for the estimated parameter values. By using this three method, the estimation of the geomechanical parameters at the karaj subway, line 2 illustrated. The results showed the fuzzy system tuned by the particle swarm optimization with the Mean sum of Squares of the Errors (MSE) of 0.0065 had the best performance.