Numerical modeling is one of the tools that can be used for designing an optimal hydraulic fracturing treatment. One approach is to solve a fully 3D problem of fracture propagation numerically. However, numerical solution of the latter problem is computationally expensive and may preclude one to use it for problems involving optimization or sensitivity analysis. At the same time, there are more specialized models that typically rely on a series of assumptions, but are substantially faster to run. For instance, such models include plane strain, radial, Perkins-Kern-Nordgren (PKN), and pseudo-3D (P3D) hydraulic fractures. The primary aim of this talk is to present a numerical model that extends the aforementioned specialized models for a single fracture into the hydraulic fracturing simulator for multiple cracks. This is done by developing an algorithm for a single fracture, which is then extended to multiple cracks. The numerical algorithm utilizes a fixed mesh approach, in which fracture grows by extension of the tip elements that are eventually split into two parts. Tip element extension utilizes the universal asymptotic solution that originates from the problem of a semi-infinite crack, which includes the effects of toughness, fluid viscosity, and leak-off. The algorithm has been tested against the solution for a plane strain hydraulic fracture in different regimes. In addition, the approach has been extended and tested against enhanced PKN and enhanced P3D models. One of the advantages of the developed model is the fixed mesh methodology, which enabled us to extend the model to multiple fractures that can change their direction of propagation with time. Extension to multiple fractures poses an additional challenging problem of solving for the elastic interaction between the cracks. To address this problem, we use Displacement Discontinuity Method, which has been modified by using elliptical fracture elements. To check accuracy of the developed simulator, its predictions are compared to the reference solution, that is computed using Implicit Level Set Algorithm.