  Using Ginzburg-Landau formalism, we theoretically study the isothermal shear
modulus anomaly of an unconventional superconductor with a multicomponent order
parameter, when the superconducting transition is split by a symmetry-breaking
field. Experimental signatures are proposed for both chiral and nematic
superconductors. Particularly striking is the vanishing of $C_{66}$ across the
lower transition to a nematic superconducting state. Our findings can guide
future experiments and shed new lights on materials such as Sr$_2$RuO$_4$ and
$M_x$Bi$_2$Se$_3$.
