Error field (or externally applied helical field) penetration is studied numerically based on the two fluids equations. It is shown that there is a minimum in the required field amplitude when the applied helical field frequency is the same as the mode frequency being determined by both the background equilibrium plasma rotation and the diamagnetic drift. The mode penetration threshold significantly increases as the field frequency deviates from the mode frequency and can become asymmetric on the two sides of the minimum due to parallel heat transport. After mode penetration the nonlinear saturated island width is found to be smaller for a larger electron diamagnetic drift frequency.