The experimental and numerical modeling of curvilinear propagation of hydraulic fractures driven by viscous fluid is implemented. The trajectories of simultaneous growth of 2-5 fractures from the boundary of a circular opening are presented in plane elasticity. The influence of the fluid viscosity on the fracture trajectory is analyzes. The causes of initiation of main fracture and shut-down of other fractures are revealed. The attempts are made to find such conditions that simultaneous growth of a few main fractures is possible by varying lengths and orientation angles of initiation fractures in the external nonuniform field of compression. The experimental modeling of hydraulic fractures was carried out using blocks made of concrete and organic glass. There were 3 to 5 initiation fractures. The influence of the breakdown fluid viscosity on the number of the main fractures is illustrated. Hydraulic fracturing with a plastic material allowed simultaneous growth of 3 and 4 fractures within a block. The experimental modeling data and the calculation results are compared.