This paper is dedicated to the identification of constitutive parameters of elasto‐viscoplastic constitutive law from measurements performed on deep underground cavities (typically tunnels). This inverse problem is solved by the minimization of a cost functional of least‐squares type. The exact gradient is computed by the direct differentiation method and the descent is done using the Levenberg–Marquardt algorithm. The method is presented for lined or unlined structures and is applied for an elastoviscoplastic constitutive law of the Perzyna class. Several identification problems are presented in one and two dimensions for different tunnel geometries. The used measurements have been obtained by a preliminary numerical simulation and perturbed with a white noise. The identified responses match the measurements. We also discuss the usage of the sensitivity analysis of the system, provided by the direct differentiation method, for the optimization of in situ monitoring. The sensitivity distribution in space and time assess the location of the measurements points as well as the time of observation needed for reliable identification.