We propose the possible detection of broken mirror symmetries in correlated two-dimensional materials by elastotransport measurements. Using linear response theory we calculate the shearconductivity \Gamma_{xx,xy}, defined as the linear change of the longitudinal conductivity \sigma_{xx} due to a shear strain \epsilon_{xy}. This quantity can only be non-vanishing when in-plane mirror symmetries are broken and we discuss how candidate states in the cuprate pseudogap regime (e.g. various loop current or charge orders) may exhibit a finite shearconductivity. We also provide a realistic experimental protocol for detecting such a response Show Partial Abstract