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This paper presents a simple, three stage method to simulate the mechanics of wetting of porous solid objects, like sponges and cloth, when they interact with a fluid. In the first stage, we model the absorption of fluid by the object when it comes in contact with the fluid. In the second stage, we model the transport of absorbed fluid inside the object, due to diffusion, as a flow in a deforming, unstructured mesh. The fluid diffuses within the object depending on saturation of its various parts and other body forces. Finally, in the third stage, oversaturated parts of the object shed extra fluid by dripping. The simulation model is motivated by the physics of imbibition of fluids into porous solids in the presence of gravity. It is phenomenologically capable of simulating wicking and imbibition, dripping, surface flows over wet media, material weakening, and volume expansion due to wetting. The model is inherently mass conserving and works for both thin 2D objects like cloth and for 3D volumetric objects like sponges. It is also designed to be computationally efficient and can be easily added to existing cloth, soft body, and fluid simulation pipelines.