During drilling, the mud column sustains a slightly higher pressure than the formation to maintain the stability of the well wall, which causes the mud filtrate to penetrate into formation pores and displace in-situ fluids. The invasion depth is affected by reservoir properties, especially the reservoir permeability. Therefore, it is possible to estimate the reservoir permeability if the invasion depth can be measured. A numerical study was conducted to investigate the feasibility of evaluating reservoir permeability with array induction logging. A mud invasion model was built up by coupling mud cake growth with multiple-phase fluid flow ,and an array induction logging model was established based on the Born geometric factor theory. Joint forward simulations of mud invasion and array induction logging indicated that the responses of array induction logging can reflect the effect of mud invasion on the formation resistivity. Inversion based on the damped least square method revealed that the invasion depth can be acquired from array induction logging data. We investigated the association between reservoir permeability and invasion depth, and found that in a reservoir with a permeability of 1 to 100mD(1 mD= 0.987×10-3μm～2),the reservoir permeability governs the invasion depth, and thus the permeability can be evaluated according to invasion depth. A two-dimensional numerical simulation showed that the inversed invasion depth curve had a similar fluctuation to the permeability variation. For a layered formation, a series of interpretation charts can be produced to evaluate the permeability of every layer with tolerable errors. The numerical investigation proves the feasibility of estimating reservoir permeability with array induction logging.