Lateral strain of uniaxially tensioned membrane

Which software do you use ? In general there are two ways to calculate lateral (transverse) strain in FEA:

a) use predefined variable - all FEA programs have strain tensor components available for postprocessing, just choose the right one (normal strain in lateral direction, for example epsilon_XX). You can either make a contour plot of it or probe its value in selected point. In your case the latter should be enough. You can plot it vs load increment. Just remember to choose some point in the middle between the supports so that they don't influence the result.

b) calculate lateral strain manually - measure displacement of selected point (as described above) in proper direction and then divide it by original dimension.