This paper presents a model based motion control approach for industrial robots by considering a serial two-link robot arm model with joint nonlinearities. In order to achieve the desired performance using the model based control approaches, it is important to obtain relevant models of both kinematics and dynamics including nonlinear characteristics. Main nonlinear components that lead to trajectory tracking errors of typical multi-axis industrial robot are joint nonlinearities in each axis and dynamic coupling effects between different axes. In this paper, a parametric modeling approach is introduced to reproduce behaviors of a serial two-link robot arm with joint nonlinearities. Nonlinear stiffness, angular transmission errors, and friction in these two links are directly identified as joint nonlinearities. This approach is applied for the serial two-link arm of a typical multi-axis industrial robot, which has low frequency vibration modes and significantly affects to the trajectory performance. Effectiveness of the modeling is verified by comparative studies with numerical simulations and experiments. Finally, a 2-DOF control scheme with the identified two-link dynamic model and a feedback loop-shaping with a variable notch filter are applied to improve the performance of trajectory tracking and residual vibration suppression.