This　paper　presents　a　theoretical　investigation　on　the　finite　time　thermodynamic　performance　for　an　irreversible　Brayton　cycle　heat　pump　(BCHP)　coupled　to　counter-flow　heat　exchangers.　The　heating　load　density,　i.e.　the　ratio　of　heating　load　to　the　maximum　specific　volume　in　the　cycle,　is　taken　as　the　optimization　objective.　Relations　between　heating　load　density　and　pressure　ratio　and　between　COP　(coefficient　of　performance)　and　pressure　ratio　for　BCHP　in　which　the　irreversibilities　of　heat　resistance　losses　in　the　hot　and　cold-side　heat　exchangers　and　non-isentropic　losses　in　the　compression　and　expansion　processes　are　derived.　The　analytical　expression　obtained　for　the　cycle　performance　enabled　its　optimization　through　addressing　the　effects　of　mechanical　and　thermal　inefficiencies　of　all　components　comprising　the　cycle.　The　influences　of　the　temperature　ratio　of　the　reservoirs,　the　efficiencies　of　the　compressor　and　expander　and　the　effectiveness　of　the　heat　exchangers　on　the　heating　load　density　are　provided.　The　cycle　performance　optimizations　are　performed　by　searching　the　optimum　distribution　of　heat　conductance　of　the　hot-　and　coldside　heat　exchangers　for　the　fixed　total　heat　exchanger　inventory　and　the　optimum　heat　capacity　rate　matching　between　the　working　fluid　and　the　heat　reservoirs.　The　BCHP　design　with　heat　loading　density　optimization　leads　to　a　smaller　size　of　all　equipments　comprising　the　heat　pump.　(C)　2011　Elsevier　Inc.　All　rights　reserved.