In this paper, we propose an effective solution to reconstruct solid models of existing objects. Specifically, we convert the model reconstruction problem into the issue of feature parameter extraction, and thereby design diverse methods to extract the parameters of basic design features from input surface meshes. After extracting the feature parameters, the corresponding features are constructed. By performing modeling operations on those features, the final solid model is constructed, and meanwhile the complete history of the model building operations is recorded. By introducing the concepts of “feature,” “constraint,” and “modeling history” into the reconstruction process, the design intent is captured and hence represented in the reconstructed model. As a result, the model is geometrically accurate and topologically consistent, and moreover it is flexibly editable, which makes it convenient to carry out model redesign and modification for the innovation applications. A variety of experimental results demonstrate the effectiveness and robustness of this solution.