Trickle Bed Reactors Are Widely Used in Many Process Industries. the Catalyst Particles Are Often Incompletely Wetted Especially in the Trickling Flow Regime and Hence to Design These Reactors, the Effectiveness Factor of Partially Wetted Catalyst Needs to Be Calculated Accurately. Numerical Solutions by Traditional Methods Are Time Consuming and Not Very Accurate, Especially for Some Commonly Used Complex Catalyst Shapes Such as Trilobes, Quadrilobes Etc. the Paper Presents a Novel Numerical Solution for These Problems based on the Method of Fundamental Solutions. the Advantage of the Method is that It Involves Only Boundary Collocation and Can Be Applied to Catalysts of Any Shape. Further the Method Provides an Accurate Estimate of the Gradient of the Concentration Profiles and This Information Can Be Related Directly to the Effectiveness Factor. This Accuracy of the Method is Demonstrated for Two Dimensional (2-D) and Axisymmetric Problems for a Linear Kinetics. Illustrative Results Are Presented for Some Complex Shapes under Partial Wetting Conditions. © 2003 Elsevier Science Ltd. All Rights Reserved.