In order to calculate the limit bearing capacity of subgrade in the karst areas, combining the theorem of the limit analysis with finite element method, the computation procedure was provided based on MATLAB. The modified Hoek-Brown criterion was adopted to describe the non-liner characteristic of the rock mass, which was also embedded into the computation procedure. On this basis, dimensional parameters Nσ and η were defined to estimate the effect of voids on the bearing capacity of subgrade, and the effect of different parameters was also analyzed in detail. The results reveal that Nσ non-linely increases with increasing the values of D/L (the ration of thickness to span) and GSI (the geological strength index), and decreases with increasing the value of H/L (the ratio of height to span), and the linear relation between Nσ and mi. The value of η first increases, then decrease with an increase in the value of α, when D/L has smaller values. The value of α (rotation angle) has a little influence on η, when D/L has larger values. The physical mechanics parameters (GSI, mi and γ) of rock mass has a negligible effect on η. The failure mechanics could be classified punch failure of roof, combined roof punch and side wall failure, combined roof falling and side wall failure. The results of bearing capacity for strip footing on a rock mass are compared with previous study, and the difference within 3%. This indicates that the method proposed in this paper is correct. Meanwhile, for the convenience of design in engineering practice, design tables are provided, which could be meet most requirements in engineering practice.