Aging effect for the ultimate strength of offshore structure is studied in this paper. A frame model of offshore structure is used, which is simplified from an actual offshore structure of jacket type. As an aging effect, corrosion due to wave, wind, current, tide, etc is considered. The history of collapse and the ultimate strength of the frame model are analyzed by using the idealized structural unit method (ISUM), for the concentrated load such as collision by a ship or an iceberg, changing the angle of collision. The analyses are performed for the initial state in which the pipe members of the frame model have the original sizes, and for the deteriorated condition in which the members are corroded and their thicknesses are reduced. The collapse behaviors (collapse modes) and the characteristics are clarified for the above various conditions. They are different depending on the angle of the collision even if the location of collision is the same. They change with the reduction of thickness of the members due to corrosion. The ultimate strength decreases proportionally to the reduction of strength of the member which is the cause of the collapse of the model, if the collapse mode does not change. But, it is possible that the ultimate strength decreased largely, if the collapse mode changes due to corrosion. The reduction of strength of the member is almost proportional to the reduction of thickness of the member. The maximum and minimum ultimate strengths of the frame model after corrosion can be estimated, using the maximum and the minimum of the ratio of reduced thickness to the original thickness of all the members in the frame model. The next second report, the frame model very close to an actual offshore structure of jacket type will be used to verify widely the characteristics and the estimating method of the ultimate strength obtained in this study.