In this paper, the loop structure of plain knitted fabric, constructed from multifilament yarns is geometrically modeled. This model is based on post-buckling behavior of multifilament yarns composed of two, three or seven filaments with circular cross sections. In the first step, the classic theory of Elastica 2-D post-buckled shape of each filament position on the yarn structure was investigated. In this step, volumetric intersections between filaments on the yarn occurred. In the Second step, the arrangement of the filaments in 3-D space was predicted applying an out-plane bending force. To find the minimized bending force and reducing the volumetric intersections between filaments, we used genetic algorithm. Genetic Algorithm was used for reducing the problem complexity and optimizing that complexity by replacing contact forces between filaments with a concentrated out-plane force. The geometry position of yarn filaments is also modeled using finite element method. Comparison of results shows small difference between the two models and confirms that the analytical proposed model is acceptable.