This article presents the development of a finite element model, which considers stochastic tow waviness using a Markov Chain algorithm and non-linear material properties using Binary Model, to predict the stress–strain and fracture behaviour of plain-weave ceramic matrix composites under uniaxial extension. The stochastic waviness is described by fluctuations in the centroid coordinates of tow positioning. The tow deviations are generated by marching sequentially from one grid point to next along a tow path. The deviations depend only on the deviation of the previous point using a probability transition matrix. A non-linear orthotropic constitutive model was implemented in a commercial finite element code Abaqus using a user-defined subroutine. Two 2 × 2 unit cell models of a plain-weave ceramic matrix composite laminate are created using stochastic tow elements generated by the virtual specimen generator, which was developed on the basis of the Markov Chain algorithm. A comparison has been made between the systematic and stochastic models to assess the effects of stochastic tow waviness on the stiffness and strength of the laminate. The numerical results have been validated by the comparison of predictions with the experimental data. The stochastic model which considers random waviness correlates well with the experimental data.