The specificity of the offshore pipelines modeling on the Arctic shelf relates to the low ambient temperature close to the freezing temperature. For example, the water temperature of the Barents Sea at the depths of about 50 meters goes down to -1,9 Celsius in some areas, while the freezing temperature for the salt water of the Barents Sea (with salinity of approximately 35 ‰) is about -1,914 Celsius. This leads to possible glaciation of the subsea structures. Gas pumping through long pipelines requires high inlet pressures. The authors have developed the mathematical models and appropriate software systems, taking into account these features. In the present paper the one-dimensional mathematical model of unsteady nonisothermal flow of a gas mixture in the hyper-pressure pipelines in northern seas and the effective numerical algorithms for calculation using the developed model are proposed. These algorithms have been realized as software packages. The mathematical model includes a model of pipeline glaciation dynamics. The developed software packages make it possible to compute the unsteady flow characteristics as well as to find the thermophysical characteristics of growing sea ice on the outer surface of a pipeline. The paper presents examples of calculating the temperature, pressure of nonisothermal unsteady flow, as well as the thickness of the sea ice layer on the outer surface of the pipeline using the parameters that are interesting for practical design of the offshore pipelines in the Barents Sea.