This work was motivated by questions raised from multifrequency microwave interferometer measurements taken in a cylindrical plasma on the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) project. Standard data analysis based on a thin beam model neglecting refraction yields inconsistent electron densities and density profiles for different frequencies. This work focuses on the development of a model for the wave propagation through cylindrical plasmas when the plasma radius is on the order of the beam waist. For the calculations presented a Gaussian beam profile and plasma spatial profile were assumed. Both refraction by density gradients and finite beam sizes are found to play important roles and explain polychromatic differences in the electron densities and profiles. Calculations for the new model are compared to a thin beam model not accounting for refraction and experimental data from VASIMR.