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, which do not comprehensively examine the nuanced process of 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 to explicitly model legal reasoning in the analysis of Chinese tort-related civil cases. We first operationalize the legal reasoning process in tort analysis into the three-module LexChain framework, with each module consisting of multiple finer-grained sub-steps. Informed by the LexChain framework, we introduce the task of tort legal reasoning and construct an evaluation benchmark to systematically assess the critical steps within analytical reasoning chains for tort analysis. Leveraging this benchmark, we evaluate existing 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 LexChain-style reasoning through prompting or post-training. The proposed baselines achieve significant improvements in tort-related legal reasoning and generalize well to related legal analysis tasks, demonstrating the value of explicitly modeling legal reasoning chains to enhance the reasoning capabilities of language models.