Legal reasoning is a fundamental component of legal analysis and decision-making. Existing computational approaches to legal reasoning predominantly rely on generic reasoning frameworks such as syllogism and IRAC, which do not comprehensively examine the nuanced processes that underpin legal reasoning. Moreover, current research has largely focused on criminal cases, with insufficient modeling for civil cases. In this work, we present a novel framework for explicitly modeling legal reasoning in the analysis of Chinese tort-related civil cases. We first operationalize the legal reasoning processes used in tort analysis into the LawChain framework. LawChain is a three-module reasoning framework, with each module consisting of multiple finer-grained sub-steps. Informed by the LawChain framework, we introduce the task of tort legal reasoning and construct an evaluation benchmark, LawChain$_{eval}$, to systematically assess the critical steps within analytical reasoning chains for tort analysis. Leveraging this benchmark, we evaluate state-of-the-art large language models for their legal reasoning ability in civil tort contexts. Our results indicate that current models still fall short in accurately handling crucial elements of tort legal reasoning. Furthermore, we introduce several baseline approaches that explicitly incorporate LawChain-style reasoning through prompting or post-training. We conduct further experiments on additional legal analysis tasks, such as Legal Named-Entity Recognition and Criminal Damages Calculation, to verify the generalizability of these baselines. The proposed baseline approaches achieve significant improvements in tort-related legal reasoning and generalize well to related legal analysis tasks, thus demonstrating the value of explicitly modeling legal reasoning chains to enhance the reasoning capabilities of language models.