This book constitutes the thoroughly refereed post-conference proceedings of the Second International Conference on High Performance Computing in Science and Engineering, HPCSE 2015, held in Soláň, Czech Republic, in May 2015. The 14 papers presented in this volume were carefully reviewed and selected from 21 submissions. The conference provides an international forum for exchanging ideas among researchers involved in scientific and parallel computing, including theory and applications, as well as applied and computational mathematics. The focus of HPCSE 2015 was on models, algorithms, and software tools which facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications. .