. The object-ive 01 t.his research is t.o minimize t.he error andcomput.at.ional t.ime 01 t.he Boundary Element. Met.hod (BEM)In t.he f’i r-s t. part- 01 t.he research, a det.ailed descript.ion 01the BEM is given, start.ing f r-orn t.he analyt-ical derivat-ion 01 t.heboundary int-egral equat.ion t-o t-he capabili t.ies of t.his met.hod int-he descript-ion of complex geomet-ries and mult-i layered domainsIn t-he second p a r-t., a review 01 t.he work done using t-he BEM,is given. This work ranges f r-orn a minimizat.ion 01 error in t-heBEM,po t.e rrt.i ed,heat.dillusion,t-oitsapplicat-iont.owavepropagation, elect.rical and mechanical problems .In t.he third part. 01 t.he work, t.wo modiIications t.o t.he BEl-!are proposed; in order t.o reduce t.he error1- A variation in Le g e rrdr-e polynomial order using a scalingproblems associated with the steel corrosion, handling due to excessive sizeand weight, undesirable formation of welds, partial composite action withthe surface concrete and deboding, lead to the need for alternativematerials, and further research in this field. The high strength to weightratio, resistance to electro-chemical corrosion, larger creep strain, goodfatigue strength, potential for. decreased installation costs and repairs due tolower weight in comparison with steel, non-magnetic and non-metallicproperties of carbon fib er reinforced polymer (CFRP) composites offer aviable alternative to bonding of steel plates. The emergence of high strengthepoxies has also enhanced the feasibility of using CFRP sheets and fabricfor repair and rehabilitation.The mam objective of this thesis is to give better and fullunderstanding of the flexure behaviour of rectangular reinforced concretepre-cracked beams strengthened with Carbon Fiber Reinforced Plastics(CFRP) sheets.The experimental program involved testing fourteen R.C. rectangularbeams. They were designed to fail in flexure and tested under flexure in( ii )