Synthetic aperture radars (SAR) data plays an important role in remote sensing applications. It is common knowledge that SAR image amplitude pixels can be approximately modeled by the Rayleigh distribution. However, this model is contin-uous and does not accommodate points with non-zero prob-ability, such as a null pixel amplitude value. Thus, in this paper, we propose an inflated Rayleigh distribution for SAR image modeling that is based on a mixed continuous-discrete distribution and can be used to fit signals with observed values on [0, infty). The maximum likelihood approach is considered to estimate the parameters of the proposed distribution. An empirical experiment with a SAR image is also presented and discussed. © 2022 IEEE.