The single crystal yield surfaces (SCYS) of bcc metals for symmetric slip on {110}<111> and asymmetric slip on {112}<111> systems have been analyzed and deduced. The complete SCYS have been derived when their critical resolved shear stresses (CRSS) are specified in a particular case (such as for Mo metal). The results showed that there are 600 stress states that can be classified into 35 groups according to the crystal symmetry. Each group activates eight, six or five {110}<111> and {112}<111> slip systems depending on crystallographically nonequivalent slip systems groups. Among all these stress states, three groups activate eight systems, there are 24 stress states; four groups activate six systems, there are 48 ones; the remaining twenty-eight groups activate five systems, there are 528 ones. In this case, the fraction of vertices for which there is slip ambiguity (more than five pure {110}<111> slip. The complete SCYS have been derived when their symmetrically slip on {110} <111> and asymmetric slip on {112} <111> systems have been analyzed and deduced. (CRSS) are specified in a particular case (such as for Mo metal). The results showed that there are 600 stress states that can be classified into 35 groups according to the crystal symmetry. Each group activates eight, six or five {110} <111> and {112} <111> slip systems depending on crystallographically nonequivalent slip systems groups. Among all three stress states, three groups activate eight systems, there are 24 stress states; four groups activate six systems, there are 48 ones; the remaining twenty-eight groups activate five systems, there are 528 ones. In this case, the fractio n of vertices for which there is slip ambiguity (more than five pure {110} <111> slip.