How does price-elasticity of supply affect the incidence of tax on consumer and producer From what I've read only price-elasticity of demand (PED) (not price-elasticity of supply (PES)) affects the burden of tax on the consumer/producer. However, my graphs suggest PES does affect it. Why is this??

(The red lines represent the supply curves of firms with elastic PES and the blue lines are for inelastic PES. The S1 lines show supply before tax and S2 shows supply post tax. I have used a demand curve with unitary PED.)

According to the graph the proportion of tax paid by the consumer on goods with price elastic supply (P1P2AB out of P3P2AC)is significantly greater than the proportion paid on goods with inelastic PES (P1P2DE out of P3P2DF. Why is this?
You are right: both the price-elasticity of demand and the price-elasticity of supply affect the respective proportions for producers and consumers of the burden of a per unit tax imposed on sales by producers.  

The proportions depend on the relative slopes, which reflect price-elasticities, of the demand and supply curves. Considering the elastic supply case in your diagram, the slope of the demand curve between points AE is much steeper than that of the supply curve between CE.  Hence E is much closer, in the vertical (price) dimension, to C than to A. Thus the post-tax price to consumers (p2 corresponding to A) is much further from the pre-tax price (p1 corresponding to E) than is the post-tax price to producers (p3 corresponding to C),and so most of the burden falls on consumers.  For the inelastic supply case the position is reversed.  A detailed explanation may be found in this NTRC paper (see section III).