In various applications of stretchable electronics and soft robots, soft materials are subjected to long-term load-bearing conditions, requiring them to possess good extreme mechanical properties such as highly stretchable, strong, fracture-resistant and anti-fatigue. Conventional soft materials with a single polymer network typically exhibit relatively low fracture resistance, while commonly employed toughening method involves introducing mechanical dissipation into original polymer networks often require complicated chemical synthesis and result in significant hysteresis under cyclic loads. Designing soft solid materials into soft network materials with periodic lattice structure paving another effective route to improve the fracture-resistant performance of soft materials, which has not been reported in the literature. This work provides a combined experimental and computational study on the mechanical properties and fracture behaviors of elastomer-based soft network materials with/without a precut crack under monotonic and cyclic loads, aiming to present a structural design strategy for fracture-resistant soft materials. The elastomer-based soft network materials are proven to be crack-insensitive, low-hysteresis and anti-fatigue. The nonlinear finite element analysis (FEA) is employed to reveal the underlying mechanism of crack-insensitivity in elastomer-based soft network materials. Both the mechanical properties and deformed configurations of soft network materials with/without a precut crack are accurately predicted by the FEA method. The effect of microstructure geometry and network topology on the mechanical properties of soft network materials is systematically studied. Under various amplitudes of cyclic applied strain, the elastomer-based soft network materials can survive even after individual microstructures ruptured, and the fatigue fracture process slows down as the applied strain amplitude decreases. In contrast to the behavior observed in monotonic loads where fracture initiates at the microstructure located ahead of the crack tip, fatigue fracture initiation in soft network materials with a precut crack exhibits a random distribution.