This paper presents an extension of Gaussian process implicit surfaces (GPIS) by the introduction of geometric object priors. The proposed method enhances the probabilistic reconstruction of objects from three-dimensional (3-D) pointcloud data, providing a rigorous way of incorporating prior knowledge about objects expected in a scene. The key ideas, including the systematic use of surface normal information, are illustrated with one-dimensional and two-dimensional examples, and then applied to simulated and real pointcloud data for 3-D objects. The performance of our method is demonstrated in two different application scenarios, using complete and partial surface observations. Qualitative and quantitative analysis of the results reveals the superiority of the proposed approach over existing GPIS configurations that do not exploit prior knowledge.