Article is devoted to the problem of developing software support of preliminary and judicial investigation of murder cases. The study of the investigative and judicial practice of murder cases shows that relevant to the investigation of murder cases is the use of mathematical and cybernetic methods. In particular, this refers to the development and introduction in investigative practice computer programs providing the investigation process algorithmization, shorter period of investigation, effective, focused casework, improvement of murder cases investigation. The authors determine the necessity of using situational approach as the basis for developing a program for preliminary and judicial investigation of murder cases of murder. The notion of investigation situation in murder cases has been identified; its content and importance for the investigation of murder cases have been considered. The logical approaches to developing such program are described. We justify the use of a computer program during the preliminary investigation of murder cases.