Summary: The remeshing algorithm based on the bubble packing method (BPM) is developed for finite element analysis (FEA) because the optimal position of nodes can be obtained systematically when only the bubble size function is given. The triangular meshes are generated by Delaunay triangulation with the advancing front concept. To use the automatically generated mesh information in FEA, a new bandwidth minimization scheme with high efficiency in CPU time is also developed. A refining circle is proposed to specify the refinement area using the bubble size in the remeshing step. The remeshing algorithm is applied to the metal forming problem to replace the distorted mesh at the largely deformed area with regular and fine meshes. The numerical results show that the remeshing algorithm based on the BPM works well at the region with large error and is able to control the refinement area and the new mesh size easily through two parameters (\(\eta_{\max}^{*},q\)).