In this work, we propose a novel method to synthetically generate realistic 3D representations of wooden logs. Efficient sawmilling heavily relies on accurate measurement of logs and the distribution of knots inside them. Computed Tomography (CT) can be used to obtain accurate information about the knots but is often not feasible in a sawmill environment. A promising alternative is to utilize surface measurements and machine learning techniques to predict the inner structure of the logs. However, obtaining enough training data remains a challenge. We focus mainly on two aspects of log generation: the modeling of knot growth inside the tree, and the realistic synthesis of the surface including the regions, where the knots reach the surface. This results in the first log synthesis approach capable of generating both the internal knot and external surface structures of wood. We demonstrate that the proposed mathematical log model accurately fits to real data obtained from CT scans and enables the generation of realistic logs.