Flexible origami is suitable for designing deployable mechanisms due to its ability to transform from a flat or compactly folded geometry to a more extended geometry. Non-Euclidean origami can help by splitting folding branches of origami vertices, leading to kinematically determinate behaviour. This paper presents two novel finite element modelling procedures for analysing flexible non-Euclidean origami, fabricated using 2D manufacturing techniques. The finite element modelling procedures presented in this work are a step towards the implementation of flexible non-Euclidean origami in functional applications, such as deployable mechanisms.