Flag has been in use for various purposes since around 5000 B.C. in Egypt. National flag evolved however in the Middle Ages while the use of flags on vessels could be said to have started around the 16th century in Spain. Flags on ships had been mainly for identification and as a political symbol but beginning from the 20th century the choice of flag to fly on a particular vessel equally requires some economic considerations. The shipowner has three different registries with different conditions for ship registration to make a choice. But he tends to find himself in a serious fix. The choice is surrounded by certain constraints which in some cases are common to all the three or gradually becoming common to all, but with other constraints being peculiar to a particular kind of registry. In this paper, a model has been developed tin flagging to portray the shipowner`s dilemma under array of constraints. This may help in decision making process by governments on matters affecting shipping and by shipowners and their advisers on ship registration.