Wound closure apparatus is provided having a force-transmitting surface operable to be placed in a proximal, external, wound-closing position on a patient, together with a force-exerting assembly operable to exert a wound-closing pressure against the patient's tissue. The force-transmitting surface is preferably three-dimensionally asymmetric to generate different forces along the length of the surface. The apparatus is especially designed for the closure of wounds attendant to endovascular interventions, e.g., a femoral artery puncture wound. The apparatus is positioned and operated so as to partially close the patient's artery upstream of the arteriotomy. The apparatus and methods hereof may also be used for the closure of wounds created during venous intervention procedures. A smaller wound closure apparatus is provided for the closure of brachial and radial wounds, and has a wrist or arm strap for securing the apparatus onto the wrist or bicep region of a patient.