The shapes of machined surfaces play a critical role affecting powertrain performance, and therefore, it is necessary to characterize the shapes with high resolution. State-of-the-art approaches for surface shape characterization are mostly data-driven by interpolating and extrapolating the spatial data but its precision is limited by the density of measurements. This paper explores the new opportunity of improving surface shape prediction through considering the similarity of multiple similar manufacturing processes. It is a common scenario when the process of interest lacks sufficient data whereas rich data could be available from other similar-but-not-identical processes. It is reasonable to transfer the insights gained from other relevant processes into the surface shape prediction. This paper develops an engineering-guided multitask learning (EG-MTL) surface model by fusing surface cutting physics in engineering processes and the spatial data from a number of similar-but-not-identical processes. An iterative multitask Gaussian process learning algorithm is developed to learn the model parameters. Compared with the conventional multitask learning, the proposed method has the advantages in incorporating the insights on cutting force variation during machining and is potentially able to improve the prediction performance given limited measurement data. The methodology is demonstrated based on the data from real-world machining processes in an engine plant.