The equation of motion of massive spherical shell expanding in the field of its own gravitational potential has been solved within the special relativity mechanics, assuming fixed total energy of such system. The initial velocity of such ``shell-universe'' is always finite and equal to the velocity of light. When the total energy is less than the rest mass energy of the shell, the expansion terminates in time and the shell collapses, while otherwise it expands indefinitely; at long times it resembles the Friedman model of universe. For zero total energy the shell radius goes in time t as \sin  (\Omega  t), where the ``frequency''  \Omega  is proportional to the rest mass of the shell. A given ``lifetime'' of the expansion-terminated shell universe can be achieved in two ways: ``grand'' or ``small'' expansion scenarios. Another version of the model, relying explicitly on the energy--gravitational-mass equivalence, leads to similar (but not identical) predictions. The predictions of the model are compared with the predictions of the GRT ``dust shell'' model. Possible impact of this special relativity model of expanding universe on its general relativity counterpart is suggested.

PACS numbers: 98.80.Bp, 98.80.Jk, 98.80.Es