•The stochastic micromechanical properties of cement paste were predicted.•Results show good agreement with data in the literature.•Specimen with lower w/c ratio has higher and less variable strength and elasticity.•A strong size effect exists in the modulus/stress ratio of cement paste. This work presents a study of stochastic fracture properties of cement paste at the micro length scale based on a combination of X-ray computed tomography (XCT) technique and discrete lattice type fracture model. Thirty virtual specimens consisting of pore, outer hydration products, inner hydration products and anhydrous cement particles were extracted from 3D images obtained through XCT from real cement paste samples. These virtual specimens were subjected to a computational uniaxial tension test to calculate their tensile strengths and elastic moduli. The predicted stochastic strengths were analysed using Weibull statistics, showing that specimens with lower w/c ratio yield higher strength and less variability. The strength-porosity and modulus-porosity relations were investigated based on existing empirical models. It was shown that existing models can predict the properties in the studied porosity range quite accurately, with the exponential model having the highest determination coefficient among all the models for both relations. Finally, by comparing the existing data in the literate, it is found that the smaller cement paste specimens have higher modulus/tensile strength ratio, which indicates that they are able to have more strain at the peak load.