Randomness in the microstructure due to variations in microscopic properties and geometrical information is used to predict the stochastically homogenised properties of cellular media. Two stochastic problems at the micro-scale level that commonly occur due to fabrication inaccuracies, degradation mechanisms or natural heterogeneity were analysed using a stochastic homogenisation method based on a first-order perturbation. First, the influence of Young's modulus variation in an adhesive on the macroscopic properties of an aluminium-adhesive honeycomb structure was investigated. The fluctuations in the microscopic properties were then combined by varying the microstructure periodicity in a corrugated-core sandwich plate to obtain the variation of the homogenised property. The numerical results show that the uncertainties in the microstructure affect the dispersion of the homogenised property. These results indicate the importance of the presented stochastic multi-scale analysis for the design and fabrication of cellular solids when considering microscopic random variation.