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The time-dependent crack initiation from the interface free-edge of adhesively bonded axisymmetric columnar butt joints (epoxy/SUS, edge shape: 90°/90°) was investigated in detail. With the change of applied stress level, σn, the butt joints exhibited crack initiation life, tC, that varied about four orders of seconds (102–106 s). Such a clear time-dependent life property was then studied in terms of the fracture mechanics. The near-edge stress/strain field at the crack initiation was numerically evaluated with the finite element method (FEM) by applying the time-hardening creep law to the epoxy resin. It was found that the critical asymptotic stress field along the interface represented by the combination of two parameters, λσcr (creep stress singularity index) and Kσcr (creep stress intensity factor), satisfies a unique relation irrespective of (σn, tC) sets. The same tendency was also confirmed when the near-edge total strain field parameters were employed. These results indicate that the K-λ criterion, originally developed for static fracture problems, still holds its validity in the time domain.