All of our Trapeze ropes come with a Dyneema core. Our Standard and Extended bar Trapezes can be manufactured without the core if you would prefer this so please do mention when ordering.
There are pros and cons to both having a core, and not having a core in your Trapeze ropes:
A Trapeze with a Dyneema core means that the ropes will be the exact length you require and the bar will remain horizontal and stable. However a Trapeze without a core means that the ropes, both Cotton and Softline Multifilament, can stretch over use. Please note that if you have a Trapeze without a Dyneema core and you use one side more dominantly than the other, it is possible one rope will stretch slightly longer than the other. 
The benefits that our customers find with having their Trapeze without a core, is that the ropes are softer when performing drops and also easier to perform tricks and rolls within the ropes. 
One other benefit of having the core is that it does offer extra strength to the ropes, however please note that because the ropes can stretch over time, and the core does not, the ropes can stretch towards the elbows and bunch slightly. In the case of this happening we advise that the ropes are milked by running your hands along the rope from the bottom to the top to lengthen out any bunching.