We investigate interactions between thin fingers formed as a result of an instability of an advancing front in growth processes. We show that the fingers can both attract and repel each other, depending on their lengths and the mobility ratio between the invading and displaced phase. To understand the origin of these interactions we introduce a simple resistor model of the fingers. The predictions of the model are then compared to the numerical simulations of two unstable growth processes: dissolution of partially cemented rock fracture and viscous fingering in a regular network of channels.