This study examines the speckle properties of SAR (synthetic aperture radar) images of non-Gaussian rough surfaces. Three height probability density functions were considered: Gaussian, exponential, and Weibull forms, while two forms of the power spectral density were considered: self-affine fractal and exponential. Computer realizations of the rough surface ensemble samples were done, followed by a physics-based simulation of SAR complex images of the rough surface. Speckle distributions were analyzed against the fully-developed speckle model. Illustrative examples with various surface roughness scales in the context of SAR imaging are given. When the surface HPD is non-Gaussian, image speckle is no longer following the Rayleigh distribution, regardless of the PSD. The speckle of exponential HPD surface profoundly away from Ravleigh model, especially under self-affine fractal PSD.