The properties of tube wave (Stoneley wave) propagation in a fluid-filled borehole penetrating a permeable rock are modified by the presence of a mudcake which may form on the borehole wall. A theoretical description of these effects characterizes the bulk properties of the porous rock using the Biot theory and the mudcake as an elastic impermeable layer. A finite membrane stiffness simulates the mudcake partial sealing mechanism. Within the context of this model, the mudcake can reduce, but not eliminate, the permeability effects on the tube wave slowness and attenuation. Numerical examples relevant to a typical sandstone of porosity 20% and permeability 200 mD, show that (a) the membrane stiffness acts to reduce the permeability effect on slowness and on attenuation and (b) a finite thickness of mudcake shifts the phase slowness by a (nearly) frequency-independent amount, with little effect upon the attenuation. An expression for the low-frequency limit clarifies the important combinations of mudcake parameters.