Longitudinally　profiled　(LP)　steel　plates　are　plates　rolled　to　variable　thickness　along　the　rolling　direction　in　order　to　suit　practical　loading　distributions　in　construction　applications.　The　elastic　buckling　load　of　LP　steel　plates　is　different　to　normal　flat　plates　due　to　the　change　in　thickness　and　it　is　hard　to　find　analytical　solutions　to　the　governing　equation.　In　this　paper,　the　elastic　buckling　coefficients　of　rectangular　LP　plates　were　calculated　using　the　Galerkin　and　Rayleigh-Ritz　method　(GRM).　The　plates　were　under　uniform　compression　and　four　typical　boundary　conditions　were　considered.　The　element　expression　of　the　feature　matrix　was　obtained　by　theoretical　derivation　and　the　elastic　buckling　coefficients　were　obtained　by　calculating　the　eigenvalues　of　the　feature　matrix　numerically　with　MATLAB.　Numerical　models　of　LP　plates　were　developed　to　validate　the　derivation.　Upon　validation　it　was　further　found　that　the　elastic　buckling　coefficients　of　LP　plates　can　be　approximately　expressed　by　those　of　constant　thickness　steel　plates　together　with　variable　thickness　coefficients.　A　series　of　approximation　formulae　of　elastic　buckling　coefficients　of　LP　rectangular　steel　plates　were　proposed.　Simplified　design　formulae　of　elastic　buckling　coefficients　of　LP　plates　were　proposed　for　the　first　time　to　promote　the　application　of　LP　plates　in　engineering　practice.