A simple and computationally efficient model is developed for calculation of slant path atmospheric transmittances in the microwave and millimeter spectral regions. The model deals simultaneously with absorption by oxygen and water vapor. Its accuracy is assessed for a range of atmospheric conditions for spectral intervals corresponding to the channels of the Advanced Microwave Sounding Unit. The model is found to be very accurate (</=0.001 error in transmittance) where water vapor absorption is weak. It is less accurate (~0.02 error in transmittance) at frequencies of strong water vapor absorption but should be adequate for most tropospheric sounding applications.