  We apply a recently developed stochastic method to the Shastry-Sutherland
model on 4x4 and 8x8 lattices. This method, which we call the Stochastic State
Selection Method here, enables us to evaluate expectation values of powers of
the Hamiltonian with very limited number of states. In this paper we first
apply it to the 4x4 Shastry-Sutherland system, where one can easily obtain the
exact ground state, in order to demonstrate that the method works well for this
frustrated system. We numerically show that errors of the evaluations depend
much on representations of the states and that the restructured representation
is better than the normal one for this model. Then we study the 8x8 system to
estimate energy eigenvalues of the lowest S=1 state as well as of the lowest
excited S=0 state, where S denotes the total spin of the system. The results,
which are in good accordance with our previous data obtained by the Operator
Variational method, support that an intermediate spin-gap phase exists between
the singlet dimer phase and the magnetically ordered phase. Estimates of the
critical coupling and of the spin gap for the transition from the dimer phase
to the intermediate phase are also presented.
