The present invention relates to a flexible thermoelectric module apparatus, and more particularly, to a flexible thermoelectric module apparatus including a heat sink longitudinally extending and a thermoelectric module disposed in the heat sink, in which the heat sink has a pipe-shaped body constituting a main body and a hole longitudinally formed through the center portion of the body, the thermoelectric module has a plurality of thermoelectric plates, the thermoelectric plates are plates having predetermined length and width, are arranged longitudinally in parallel with the heat sink, with a first side in the width direction connected to the inner side of the body and a second side disposed inside the hole, are arranged in parallel with each other at circumferentially predetermined distances from each other in the hole, and have a predetermined angle to the radial direction of the heat sink such that they are inclined at a predetermined angle therebetween.