  The structure of neutrino masses and mixing resulting from trilinear $R$
violating interactions is studied in the presence of the gauge mediated
supersymmetry breaking. Neutrino masses arise in this model at tree level
through the RG-induced vacuum expectation values of the sneutrinos and also
through direct contribution at 1-loop. The relative importance of these
contributions is determined by the values of the strong and weak coupling
constants. In case of purely $\lambda'$ couplings, the tree contribution
dominates over the 1-loop diagram. In this case, one simultaneously obtains
atmospheric neutrino oscillations and quasi-vacuum oscillations of the solar
neutrinos if all the $\l'$ couplings are assumed to be of similar magnitudes.
If R parity violation arises from the trilinear $\l$ couplings, then the loop
induced contribution dominates over the tree level. One cannot simultaneously
explain the solar and atmospheric deficit in this case if all the $\l$
couplings are of similar magnitude. This however becomes possible with
hierarchical $\l$ and we give a specific example of this.
