The present invention is directed to a novel polymodal asymmetric elastomeric block copolymer and a pressure sensitive adhesive and tape made therefrom. The novel block copolymer comprises from about 4 to about 40 percent by weight of a polymerized monovinyl aromatic compound and from about 96 to about 60 percent by weight of a conjugated diene. The block copolymer has the general formula Q.sub.n Y where Q represents an individual arm of the block copolymer and has the formula S-B; n represents the number of arms and is at least 3; and Y is the residue of a multifunctional coupling agent. Furthermore, S is a nonelastomeric polymer segment endblock of a polymerized monovinyl aromatic homopolymer, there being at least two different molecular weight endblocks in the block copolymer. The number average molecular weight of the higher molecular weight endblock (Mn).sub.H is in the range of from about 5,000 to about 50,000, and the number average molecular weight of the lower molecular weight endblock (Mn).sub.L is in the range of from about 2,000 to about 10,000. The ratio (Mn).sub.H /(Mn).sub.L is at least 1.25. In addition, B is an elastomeric polymer segment midblock which connects each arm to a residue of a multifunctional coupling agent (Y) and comprises a polymerized conjugated diene or combination of conjugated dienes.