Photospheric line-tying has a stabilizing effect that allows magnetic energy to build up in coronal loops until critical conditions are reached and the loop becomes unstable to them=1kink instability [1]. Recent research has concentrated on the non-linear evolution of instabilities in line-tied coronal loops. There are suggestions [2–5] that current sheets form during the non-linear evolution of the kink instability. We present 3D MHD simulations of the non-linear evolution of MHD instabilities in line-tied coronal loops. These simulations are carried out on a multi-processor cluster at St Andrews using a new 3D MHD Lagrangian remap code (Lare3d) which we shall discuss briefly. Results are presented for loops with different shear profiles to test the conditions for current sheet formation. We begin by presenting the test case of the Gold-Hoyle field, and compare our results with previous results [1,6]. New results for equilibria with no net axial current are presented and the formation of current sheets discussed. ©2000 American Institute of Physics.