A mating connection assembly permits quick and efficient connection and disconnection of tubular goods and equipment. A female box-end connection member has a body, a central through-bore, a bowl-like receptacle section having a tapered internal surface and inwardly-extending load shoulder members along the tapered internal surface, grouped in stacks of spaced-apart rows. A mating male pin-end connection member has a body section, a tapered pin extension, a central through-bore and lug members on the outer surface of the tapered pin extension. The tapered pin extension of the male pin-end connection member can be stabbed into the female box-end connection member and partially rotated. When joined in mating relationship, the connection assembly provides a fluid pressure seal, supports high-tensile axial loading and permits the transmission of torque through the connection assembly.