We present the results of a laboratory experiment on multistage hydraulic fracturing using a gel solution as the fracturing fluid, utilizing a laboratory setup for simulating hydraulic fracturing under triaxial stresses. As a result of the experiment, a fracture network was formed in a cubic rock specimen. We found that an almost planar fracture was formed during the first fracturing stage, while a concave (bowl-shaped) fracture was formed during the second stage. Interaction between the stress fields created by the two main hydraulic fractures (stress interference) caused growth of secondary cracks parallel to the simulated wellbore, but in this case led to a decrease in the width of the subsequent main fracture. We established that the penny-shaped fracture model is more suitable for predicting the geometry of hydraulic fractures in horizontal wells than two-dimensional (rectangular) fracture propagation models (the Perkins - Kern - Nordgren (PKN) model, the Khristianovic - Geertsma - de Klerk (KGD) model). Special attention needs to be paid to fracture spacing design in multistage hydraulic fracturing in horizontal wells.