A leg wrap structure is provided in a disposable absorbent garment such as a diaper or training pants. The leg wrap structure has a base layer, a top layer, and an elastic construction disposed therebetween. The elastic construction includes a plurality of spaced apart (e.g. generally equally spaced apart) elastic elements (e.g. strands or threads) that are aligned in a generally in generally parallel relation. Further, the top and base layers define a region of inelasticity. The leg wrap structure provides for the efficient formation of a reservoir and a plurality of fluid dams each capable of capturing a quantity of fluid to minimize the occurrence of fluid leaks from the absorbent article. Methods of forming such absorbent articles are disclosed.