Extra paperwork, costs and uncertainty over future funding are causing concerns for those in the sector.
The Welsh government said it was trying to “break down” barriers while the UK government said it was committed to supporting the creative economy.
Tom Rack, artistic director of NoFit State contemporary circus company, described the effects as “a big blow”.
The company is restructuring its business model to avoid touring in the European Union, but Mr Rack said it would inevitably mean scaling back productions.
“Our European touring is a big part of our work and a major source of our income. We effectively subsidise the work we do in the UK with our European touring and that’s just been made a whole lot harder.
“We’ve seen it coming, we just need to prepare for it and do the paperwork and deal with the bureaucracy but there’s also a huge cost involved.”
Taking shows outside Europe in the past has been expensive and Mr Rack fears leaving the EU will make touring in Europe equally costly.
“£45,000 is the extra costs it took us to take one show to New York just in terms of not being inside Europe. The different regulations, having to get recertified health insurance and carnets,” he said.
“It’s a big amount of money and we operate with really small margins. It’s going to be tricky.”
Half its artists are EU citizens, so bringing them to the UK to work will be “a logistical nightmare”, according to Mr Rack.
“They will need visas and health insurance and all sorts of complicating factors and likewise if we go out with our British and Welsh artists. We’ll have to cover those extra costs.”
No Fit State, like many companies and projects within the arts sector in Wales, has benefitted from funds such as Creative Europe, the EU’s fund that invests in arts and cultural projects.
The fund has spent more than €12.4m (£11.2m) in Wales over the past seven years on media and cultural projects.
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