Parameter identification of a drill-string is studied. The system is modeled as a hyperbolic system with dynamical boundary conditions. The considered model is a wave equation with spatial dependent elasticity and viscous damping terms. The identification problem is recast as an optimization problem over an infinite dimensional space. The developped approach ensures that the estimates of the parameters lie in a given set. A gradient descent-based algorithm is proposed to generate parameters estimates based on experimental data. A thorough comparative study with more classical algorithms is presented.