Implicit surfaces are a powerful shape primitive for computer graphics. This book focuses on a shape modelling approach which generates synthetic shapes by the specification of an implicit surface generating function that has random properties. This type of graphic object can be called a stochastic implicit surface because the surface is perceived as the realisation of a stochastic process. The contributions of this book are in the form of new and improved modelling and rendering algorithms to deal with stochastic implicit surfaces. On the modelling side, a topological correction algorithm is described to detect disconnected surface parts that arise as a consequence of the implicit surface representation. A surface deformation algorithm, based on advection through a vector field, is also presented. On the rendering side, an improved ray casting method is presented that guarantees correct intersections between view rays and the surface, followed by a progressive refinement algorithm that provides an interactive rendering environment where the image quality steadily improves. An application is given in the context of the procedural modelling of a fractal planet.