Plate anchors are a well-established solution for supporting the efforts of floating platforms for wind and marine renewable energies. The behavior of ultrathin rigid plate anchors buried in purely cohesive soils under undrained and plane-strain conditions is analyzed. As already known, a dimensional analysis shows that the pull-out capacity of the anchor may be expressed using a weightless break-out factor (Nc) that only depends on the ratio between the depth and the anchor width (H/B). Using finite element analyses, tabulated values of the weightless break-out factor are provided in this paper and three different failure mechanisms are identified, namely very shallow (quasi-vertical), shallow or intermediate (semi-vertical), and deep (rotational). For very shallow failure mechanisms, the studied problem is completely equivalent to the trapdoor problem because immediate breakaway at the bottom part of the anchor is considered (vented conditions). The existing analytical solutions for the very shallow (Nc = 1.956 H/B) and deep cases (Nc = 3π + 2) using the slip-line method are reviewed and an analytical limit is proposed for the first time for the very shallow mechanism (H/B = 1.314). For shallow (intermediate) cases, the failure mechanism is identified and the angle of the main slip lines is numerically evaluated.