The paper addresses a problem of robotic manipulator calibration in real industrial environment. The main contributions are in the area of the elastostatic parameter identification. In contrast to other works the considered approach takes into account the elastic properties of both links and joints. Particular attention is paid to the practical identifiability of the model parameters, which completely differs from the theoretical one that relies on the rank of the observation matrix only, without taking into account essential differences in the model parameter magnitudes and the measurement noise impact. This problem is relatively new in robotics and essentially differs from that arising in geometrical calibration. To solve the problem, physical algebraic and statistical model reduction methods are proposed. They are based on the stiffness matrix sparseness taking into account the physical properties of the manipulator elements, structure of the observation matrix and also on the heuristic selection of the practically non-identifiable parameters that employ numerical analyses of the parameter estimates. The advantages of the developed approach are illustrated by an application example that deals with the elastostatic calibration of an industrial robot in a real industrial environment.