In　this　paper,　strategies　are　provided　for　a　powerful　numerical　manifold　method　(NMM)　with　h　and　p　refinement　in　analyses　of　elasticity　and　elasto-plasticity.　The　new　NMM　is　based　on　the　concept　of　the　independent　cover,　which　gets　rid　of　NMM＇s　important　defect　of　rank　deficiency　when　using　higher-order　local　approximation　functions.　Several　techniques　are　presented.　In　terms　of　mesh　generation,　a　relationship　between　the　quadtree　structure　and　the　mathematical　mesh　is　established　to　allow　a　robust　h-refinement.　As　to　the　condition　number,　a　scaling　based　on　the　physical　patch　is　much　better　than　the　classical　scaling　based　on　the　mathematical　patch;　an　overlapping　width　of　1%-10%　can　ensure　a　good　condition　number　for　2nd,　3rd,　and　4th　order　local　approximation　functions;　the　small　element　issue　can　be　overcome　after　the　local　approximation　on　small　patch　is　replaced　by　that　on　a　regular　patch.　On　numerical　accuracy,　local　approximation　using　complete　polynomials　is　necessary　for　the　optimal　convergence　rate.　Two　issues　that　may　damage　the　convergence　rate　should　be　prevented.　The　first　is　to　approximate　the　curved　boundary　of　a　higher-order　element　by　overly　few　straight　lines,　and　the　second　is　excessive　overlapping　width.　Finally,　several　refinement　strategies　are　verified　by　numerical　examples.