The　diffraction　of　Lamb　waves　by　a　finite　delamination　situated　on　a　random　plane　parallel　to　the　symmetric　plane　of　a　laminated　plate　is　taken　into　account.　Two　imaginary　planes　are　introduced　to　solve　the　problem　by　adopting　the　method　of　mode　matching.　By　taking　an　appropriate　finite　number　of　terms　of　the　infinite　expansion　series　and　some　selected　points　on　the　two　imaginary　planes　through　convergence　and　precision　tests,　a　matrix　equation　is　obtained　to　evaluate　the　expansion　coefficients　numerically.　Reflection　coefficients　versus　the　normalized　length　a/h　and　the　relative　location　h(1)/h　of　the　delamination　are　calculated　in　the　low-frequency　domain,　the　relative　errors　are　found　to　be　less　than　1%.　Results　obtained　indicate　that　the　theory　developed　in　this　paper　is　meaningful　for　the　detection　of　both　the　size　and　the　location　of　a　delamination　in　a　laminated　plate　by　cooperating　with　experimental　techniques　for　the　non-destructive　evaluation　(NDE)　technology.