This　study　investigates　wave　propagation　of　layered　composite　rock　mass　composed　of　multiple　joints　and　assorted　rock　materials.　Firstly,　the　effect　of　multiple-reflection　between　joints　on　wave　transmission　was　explored　by　modifying　the　method　of　characteristics.　Secondly,　the　superposition　of　direct　and　indirect　transmission　induced　by　multiple-reflection　was　analyzed.　Waveform　variations　in　wave　transmission　were　compared　across　three　different　layered　composite　rock　mass.　Finally,　the　effects　of　wave　parameters　(frequency),　joint　parameters　(stiffness　and　number),　and　rock　parameters　(wave　impedance　ratio)　on　both　direct　and　indirect　transmission　induced　by　multiple-reflection　were　considered.　The　results　indicate　that　the　effect　of　indirect　transmission　induced　by　multiple-reflection　on　both　particle　velocity　and　stress　transmission　of　waves　cannot　be　ignored　in　many　cases.　The　results　further　indicate　that　effect　of　indirect　transmission　induced　by　multiple-reflection　on　both　particle　velocity　and　stress　transmission　coefficients　decreases　with　increasing　incident　wave　frequency,　while　it　increases　with　increasing　joint　numbers.　The　effect　initially　increases　and　subsequently　decreases　with　increasing　joint　stiffness.　Furthermore,　the　effect　of　indirect　transmission　induced　by　multiple-reflection　on　the　particle　velocity　transmission　coefficient　increases　while　its　effect　on　the　stress　transmission　coefficient　decreases　with　increasing　wave　impedance　ratio.　©　2024　Elsevier　Ltd