Cellulosic materials have special advantages for transport packaging, because of their lightweight and recyclable natures and also relatively high specific strength. The strength of such materials is normally evaluated by applying monotonically increasing, quasi-static displacement (or load). However, in real circumstances, the material is subjected to far more complex loading histories, such as creep, fatigue, and random loading. Failures under such circumstances are, not only time-dependent, but also notoriously variable. For example, the coefficient of variation for creep lifetime reaches or even exceeds 100%. The objective of this study is to develop a method to characterise both time-dependent and statistical natures of failures of cellulosic materials. We have used a general formulation of time-dependent, statistical failure, originally proposed by Coleman (J Appl Phys 29(6):968-983, 1958). We have identified three material parameters: (1) characteristic strength, representing short term strength, (2) brittleness parameter (or durability), and (3) Weibull shape parameter related to long-term reliability. These parameters were determined by special protocols of creep and constant loading-rate (CLR) tests for a series of containerboards. Results have shown that these two test methods yield comparable values for the materials parameters. This implies the possibility of replacing extremely time-consuming creep tests with the more time-efficient CLR tests. Comparing the cellulose fibre networks with fibres and composites used for advanced structural applications, we have found that they are very competitive in both reliability and durability aspects with Kevlar and glass-fibre composites.