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Many soil processes and functions, including carbon storage, water and element cycling, and crop productivity, are directly or indirectly affected by soil aggregates. As a key property, aggregate tensile strength is usually quantified by the Weibull distribution. This distribution was found to depend on soil texture, organic matter content, and aggregate shape; however, effects of cementing agents (i.e., clay mineral and organic compounds) on aggregate tensile strength cannot be empirically studied independent of shape. The objective was to apply Discrete Element Modeling (DEM) to simulate the rupture of soil aggregates of different shapes but the same assumed distributions of cementing agents. The hypothesis was that the Weibull modulus of aggregate tensile strength could be used to describe the heterogeneity of the particle binding forces within the aggregate. Multiple DEM simulations of aggregate rupture were carried out for sets of randomly generated binding force distributions between particles of the same diameter. Aggregate properties and shapes were obtained from those observed in arable Gleyic Cambisol topsoil from plots with and without vegetation of a soil compaction trial; additional aggregate shapes were simulated to increase the predictive range. The simulation results showed that (i) the sensitivity of Weibull modulus of aggregate tensile strength to the heterogeneity of particle binding force distribution increased with aggregate sphericity, (ii) the value of the Weibull modulus decreased with increasing heterogeneity of this distribution, and (iii) internal heterogeneity also reduced the crack surface area produced by aggregate rupture. Results corresponded to friability theory implying that small values of Weibull modulus indicated more complex soil structural organization. The DEM simulations could help explaining complex interactions between aggregate shape cementing agents and stability. Our DEM approach also uncovered the importance of Weibull modulus to assess structural features of soil aggregates and to describe the heterogeneity of the particle binding forces within the aggregate.