An appropriate assessment of dynamical response of the marine propeller shaft is essential to enable optional power delivery to propeller and to minimize the dispensable mechanical friction of supporting bearings. The interaction behavior of the shaft-bearing system affects the stability of propulsion system seriously. An applicable numerical model regarding the friction induced vibration with velocity-dependent and stick-slip friction is proposed. The effect of smoothing factor, control factor, stick factor and slip factor which obtained with experimental data on the friction coefficient is analyzed separately. A cooperative Newton-Raphson & Newmark-β solving method is validated by experimental tests to be suitable to solve the proposed nonlinear model. To capture the nature of shaft-bearing interaction, the response of dynamic friction coefficient, relative velocity and reaction force with various model parameters are obtained. The residual of iteration which defined in the proposed solving method is also analyzed for each case to certificate the reliability of the numerical calculation. The stability analysis regarding various impact factor of the proposed shaft-bearing system is discussed with multiple scales method. An optimized design for propeller shaft and supporting bearing caused by friction induced by friction properties is thus realized based on proposed numerical model.