  We prove that under suitable conditions, the Jacobi Poincar\'{e} series of
exponential type of integer weight and matrix index does not vanish
identically. For classical Jacobi forms, we construct a basis consisting of the
"first" few Poincar\'{e} series and also give conditions both dependent and
independent of the weight, which ensures non-vanishing of classical Jacobi
Poincar\'{e} series. Equality of certain Kloosterman-type sums is proved. Also,
a result on the non-vanishing of Jacobi Poincar\'{e} series is obtained when an
odd prime divides the index.
