  We report the evolution of a charge density wave (CDW) state in the quasi-2D
rare-earth tritellurides ($R$Te$_3$ for $R$=Er,Tm) as a function of in-plane
uniaxial stress. Measurements of the elastocaloric effect, resistivity, and
elastoresistivity allow us to demonstrate the importance of in-plane
antisymmetric strain on the CDW and to establish a phase diagram. We show that
modest tensile stress parallel to the in-plane $a$-axis can reversibly switch
the direction of the ordering wavevector between the two in-plane directions.
This work establishes $R$Te$_3$ as a promising model system for the study of
strain-CDW interactions in a quasi-2D square lattice.
