This paper introduces a novel method to simulate Bmode medical ultrasound speckle in synthetic images. Our approach takes into account both the ultrasound image formation model and the speckle formation model. The algorithm first modifies the geometry of an ideal noiseless image to match that of a sectoral B-mode ultrasonogram, by subsampling a grid of pixels to simulate the acquisition and quantization steps of image formation. Then, speckle is added by simulating a random walk in the plane of the complex amplitude, according to the Burckhardt speckle formation model. We finally interpolate the noisy subsampled pixels in order to fill the space introduced by the sampling step and recover a complete image, as would a real ultrasonograph. Synthetic speckle images generated by this method are visually and theoritically very close to real ultrasonograms.