Recently, Candes and Donoho introduced the curvelet transform, a new multiscale representation suited for objects which are smooth away from discontinuities across curves. Their proposal was intended for functions f defined on the continuum plane R2. In this paper, we consider the problem of realizing this transform for digital data. We describe a strategy for computing a digital curvelet transform, we describe a software environment, Curvelet 256, implementing this strategy in the case of 256 X 256 images, and we describe some experiments we have conducted using it. Examples are available for viewing by web browser.