We investigated a coronal magnetic configuration including a semicircular flux rope with two ends anchored in the photosphere. The background field is produced by two source regions on the photosphere. We study the evolution of this configuration in response to the gradual change in the background field, which is modeled by varying either the strength of the source or the distance between the source regions on the photosphere. Our results indicate that the evolution due to the change in source strength shows the likelihood of catastrophic loss of equilibrium, and that the evolution due to the change in the distance is smooth and does not manifest any tendency to lose equilibrium. In the former case, the current sheet starts developing fairly early; it forms even before the evolution reaches the maximum current state. We notice that the effect of the curvature of flux rope on the evolution of the system is significant, such that the equilibrium curve does not form a cusp-catastrophic structure but a simple fold-catastrophic structure even if the evolution is ideal MHD and a current sheet attached to the boundary surface occurs. The curvature strengthens the magnetic compression between the flux rope and the photosphere and makes the loss of equilibrium easier. However, the question of how the system behaves after the loss of equilibrium is still open since the flux rope is not likely to remain semicircular at the stage of fast evolution.