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The capacity allocation is a practically significant factor to influence the quality of the train timetables in the rail operations, especially under the fluctuation of passenger demands. This paper aims to investigate a detailed description for the structure and characteristics of the capacity allocation problem under random demand in the high-speed rail network. A two-stage stochastic integer programming model is provided to get the capacity allocation solutions to meet random fluctuations of passenger demands in the daily operations, which incorporates demand uncertainty and makes no assumptions for the rail network structure and distribution of passenger demands. Given the inherent complexity for solving this problem, we provide a solution framework including a heuristic algorithm based on tabu search in order to obtain a near-optimal solution and strategies to obtain an efficient timetable and train formation adjustment. Finally, two sets of examples, in which a sample rail network with 5 stations and the Beijing-Shanghai high-speed rail network data are adopted as the experimental environments to illustrate the performance and effectiveness of the proposed methods. • A two-stage stochastic program model for train capacity allocation is presented. • A heuristic algorithm based on tabu search is provided to solve the problem. • A strategy for an efficient timetable and train formation adjustment is provided. • Numerical experiments are given to illustrate the proposed approaches. [ABSTRACT FROM AUTHOR]