Glaciation and thawing models of the outer surface of an offshore gas pipeline in the northern seas are presented. The glaciation model suggests a modification of the Stefan condition that allows us to account for the features of sea-ice growth in salt water. A numerical algorithm for solving an unsteady problem of glaciation (thawing) of a multilayer cylindrical area by an explicit front-tracking method and some calculation results for different versions of these problems of practical interest are given. Qualitative estimates of the feasibility of the transition to a quasi-stationary version of the glaciation (thawing) model of multilayer areas are obtained. The quantitative condition for the admissibility of using the quasi-stationary approximation in the calculations of glaciation (thawing) of a certain multilayer area is given. These estimates are important for developing effective numerical algorithms to calculate unsteady regimes of gas transportation through offshore gas pipelines. For the problems of the thawing of the surface of an offshore gas pipeline, an equation is proposed that allows us to find the minimal ice thickness under the conditions studied.