The model and algorithm for the numerical solution of the three-dimensional problem of hydraulic fracture initiation and further propagation will be presented. The model is fully coupled and takes into account three important processes: elastic deformation of the rock, fluid flow in the fracture, and its further propagation in the rock. The mathematical model consists of three groups of equations. Each of them responses for one process defined above. The elasticity equations are solved by the dual boundary element method (DBEM), the lubrication equations by the finite element method (FEM) improved by simple conservative correction. This correction allows us to preserve the total volume of injected fluid on the discrete level. The fracture propagation criterion gives the system of non-linear equations, which is solved by special modification of relaxation method. In the early stages of propagation we need to explicitly consider the fluid lag, which in general varies along fracture front. It essentially increases needed computational resources. One of the ways to overcome this challenge is to use any approximation of behavior of variables near the fracture front (tip). Are the already developed asymptotic solution applicable here? The results obtained by the model include the initiation pressure for the real configuration of perforated well, the shape of the fracture, its position and orientation, as well as the possibility of reorientation and the size of the domain where it reorients. The cementing and casing of the well can be taken into account. From the point of oilfield engineer's view, the model can be useful in the understanding of the early stage of hydraulic fracturing when there are many stop cases that sometimes lead to an unsuccessful hydraulic fracturing.