  We consider strings living in $AdS_3\times S^3\times S^3\times S^1$ with
nonzero $B$-field. By using specific ansatz for the string embedding, we obtain
a class of solutions corresponding to strings moving in the whole ten
dimensional space-time. For the $AdS_3$ subspace, these solutions are given in
terms of incomplete elliptic integrals. For the two three-spheres, they are
expressed in terms of Lauricella hypergeometric functions of many variables.
The conserved charges, i.e. the string energy, spin and angular momenta, are
also found.
