In this work we investigate the fragmentation of layers under external forces, model the systems through spring networks, and focus on the interplay between elasticity and disorder. We concentrate on thin layers on supports. Our study shows that spring-network models display universal scaling: After an initial stage, the mean fragment length (L) scales with the applied strain epsilon, (L) proportional to epsilon(-alpha) where alpha only depends on the degree of disorder in the layer and the nonlinearity in the force-elongation relation of the springs. We derive analytical expressions for a and exemplify our findings by numerical simulations. In addition, we compare the theoretical results with available experimental data.