  We construct smooth asymptotically AdS_5xS^5 solutions of Type IIB
supergravity corresponding to all the half-BPS surface operators in N=4 SYM.
All the parameters labeling a half-BPS surface operator are identified in the
corresponding bubbling geometry. We use the supergravity description of surface
operators to study the action of the SL(2,Z) duality group of N=4 SYM on the
parameters of the surface operator, and find that it coincides with the recent
proposal by Gukov and Witten in the framework of the gauge theory approach to
the geometrical Langlands with ramification. We also show that whenever a
bubbling geometry becomes singular that the path integral description of the
corresponding surface operator also becomes singular.
