This paper presents a new method for constructing quickly and automatically precision tree models from point clouds of the trunk and branches obtained by terrestrial laser scanning. The input of the method is a point cloud of a single tree scanned from multiple positions. The surface of the visible parts of the tree is robustly reconstructed by making a flexible cylinder model of the tree. The thorough quantitative model records also the topological branching structure. In this paper, every major step of the whole model reconstruction process, from the input to the finished model, is presented in detail. The model is constructed by a local approach in which the point cloud is covered with small sets corresponding to connected surface patches in the tree surface. The neighbor-relations and geometrical properties of these cover sets are used to reconstruct the details of the tree and, step by step, the whole tree. The point cloud and the sets are segmented into branches, after which the branches are modeled as collections of cylinders. From the model, the branching structure and size properties, such as volume and branch size distributions, for the whole tree or some of its parts, can be approximated. The approach is validated using both measured and modeled terrestrial laser scanner data from real trees and detailed 3D models. The results show that the method allows an easy extraction of various tree attributes from terrestrial or mobile laser scanning point clouds.