Double network (DN) gels, consisting of a brittle first and flexible second network, have been known to be extremely tough and functional hydrogels. In a DN gel subjected to force, the brittle first network breaks prior to the fracture of the flexible network. This process, referred to as internal fracture, dissipates energy and increases the energy required to completely fracture DN gels. Such internal fracture macroscopically appears as a yielding-like phenomenon. The aim of this paper is to investigate the relationship between the yield point and the first network molecular structure of DN gels to more deeply understand the internal fracture mechanism of DN gels. To achieve this goal, we synthesized DN gels having a tetra-PEG first network, which is known to be a nearly ideal and well-controlled network gel. We have found that yielding of the DN gels occurs when the first network strands reach their extension limit (finite extensibility), regardless of their deformation mode. This conclusion not only helps by further understanding the toughening mechanism of DN gels but also allows for the design of DN gels with precisely controlled mechanical properties.