Magnetoelastic effects in antiferromagnetic CuMnAs are investigated by applying dynamic strain in the 0.01% range through surface acoustic waves in the GaAs substrate. The magnetic state of the CuMnAs/GaAs is characterized by a multitude of submicron-sized domains, which we image by x-ray magnetic linear dichroism combined with photoemission electron microscopy. Within the explored strain range, CuMnAs shows magnetoelastic effects in the form of Néel vector waves with micrometer wavelength, which corresponds to an averaged overall spin-axis rotation up to 2.4∘ driven by the time-dependent strain from the surface acoustic wave. Measurements at different temperatures indicate a reduction of the wave amplitude when lowering the temperature. However, no domain wall motion has been detected on the nanosecond timescale.