The numerical manifold method (NMM) has numerous advantages for discontinuous deformation analysis. In this study

by combining NMM with the basic concept of crack tip function

we conduct hydraulic fracture simulation and analyse the failure process without the concepts of Heaviside function and level set. To avoid the error caused by different positions of the crack tip in an element

singular cover functions are added for every physical cover near the crack tip within a certain range. One example is selected to show the influence of inner water pressure on the stress intensity factor (SIF). When the force on the crack is considered

the influence of each factor on the SIF is quantitatively analysed

and then hydraulic fracture of branch crack is simulated. The results show that the improved results are in good agreement with the analytical solutions. It is found that the error is often large when the force on the crack is ignored. However

when the force on crack is considered

the error gradually decreases with increasing either crack length or mesh density. The progressive failure of the branch crack shows that the method is feasible and is of great practical value.