A new rear cone decentration model has been implemented in the cylindrical resonator optical quality (CROQ) code, which simulates the performance of the ALPHA annular resonator. The new model avoids the traditional way of using equivalent phase tilts to simulate the decentration effect of optical elements in an optical train. Instead, it uses the approach of local field shift. As a result, the new model requires fewer Fourier components to represent the azimuthal variation of fields and thus largely extends the range of rear cone decentration that can be modeled by the CROQ code. The required memory space and CPU time for each decentration case are also significantly reduced.