A critical limitation of fibre reinforced plastic is its large variability on mechanical performance, especially the longitudinal compressive strength. The influence of fibre random packing and waviness on the compressive strength of UD fibre reinforced plastic is studied in this paper. Three-dimensional geometrically non-linear finite element model is constructed to investigate the compressive behaviour, and an improved approach named Latin hypercube sampling based on random sequential expansion is proposed to generate random fibre distribution across the cross-section. Latin hypercube sampling based on random sequential expansion provides high computation efficiency and good distribution characteristics in comparison to previously proposed methods. Fibre waviness defect with different misalignment angles is also incorporated in the finite element model. It is shown that random fibre packing tends to result in a stochastic detriment of fibre reinforced plastic compressive strength in comparison with uniform fibre packing condition, and the stochastic variation of compressive strength tends to follow normal or lognormal distribution.