In　this　paper,　we　propose　a　theoretical　calculation　method　for　the　displacements　of　transient　wave　excited　by　a　linear　array　coupled　to　an　elastic　solid　with　a　longitudinal　wave　couplant.　Firstly,　the　vertical　and　horizontal　displacements　excited　by　a　vertical　line　source　are　solved　based　on　exact　and　analytical　solutions　of　transient　elastic　waves　induced　by　a　line　source　normally　acting　on　an　elastic　half-space.　Secondly,　in　this　case,　the　displacements　from　a　linear　array　can　be　determined　by　the　superposition　of　the　solutions　of　a　number　of　discrete　line　forces　mentioned　above.　All　the　theoretical　results　are　compared　to　the　finite　element　simulation　results.　The　theoretical　results　are　consistent　with　finite　element　simulation　data.　Therefore,　the　calculation　method　can　save　a　lot　of　computing　time.　This　paper　provides　a　fast　and　accurate　calculation　method　of　transient　wave　displacements　in　a　half-space　generated　by　a　linear　array.　The　calculation　method　can　be　used　to　explore　the　sound　field　characteristics　of　a　linear　array　transducer　in　the　future.　©　The　Authors,　published　by　EDP　Sciences,　2017.