The collapse of lava domes, inherently heterogeneous structures, represents a significant volcanic hazard. Numerical and analogue models designed to model dome instability and collapse have incorporated heterogeneity in the form of discrete zones with homogeneous properties. Based on an assessment of dome rock heterogeneity, we explore whether material property heterogeneity (“diffuse” heterogeneity) within these discrete zones can promote dome instability. X-ray computed tomography shows that dome samples are characterised by high microstructural heterogeneities; e.g. porosity varies from 0.07 to 0.20 over millimetric length scales. To explore how microstructural heterogeneity influences sample-scale strength, we performed numerical simulations using Rock Failure and Process Analysis. The mean mechanical properties of the numerical samples were constant, and we introduced heterogeneity by varying their distribution using a Weibull probability function. The models show that increasing heterogeneity can reduce sample-scale strength by more than a factor of 2. To explore the influence of dome-scale heterogeneity, we numerically generated lava domes in Particle Flow Code. The domes have the same bulk strength but are characterised by different degrees of heterogeneity by varying the distribution of cohesion using a Weibull probability function. The models show that a greater degree of heterogeneity induces higher dome-scale displacements and that, when there is also a discrete weakened zone, the addition of diffuse heterogeneity leads to more widely distributed deformation. Therefore, alongside discrete zones defined by different material properties, we find that the diffuse heterogeneity inherent to a dome is sufficient to compromise dome stability and should be incorporated in future modelling endeavours.