Non-axisymmetric cavities are widely used as standard blackbody sources for radiation thermometry. The integrated effective emissivity is central to the blackbody design. Integrated effective emissivities are numerically calculated for non-isothermal, non-axisymmetric cavities. The average relative deviation is 0.087% when compared with Monte-Carlo results, indicating that this method can accurately calculate the integrated effective emissivities for non-isothermal, non-axisymmetric cavities. The effects of the wavelength, temperature uniformity, and bottom inclination angle are then analyzed.