Elastic (elastic compliance) and anelastic (internal friction) properties of a particulate magnetoelectric composite (x)Mn0.4Zn0.6Fe2O4–(1 − x)PbZr0.53Ti0.47O3 (x = 0, 0.1, 0.2, 0.3, 0.4, and 0.6) at a frequency of ≈30 Hz over a temperature range from 290 to 700 K are studied. Temperature dependences of elastic compliance and internal friction near the ferroelastic Curie point are found to be well approximated by power functions. Observed dependences of exponents on the composite composition are associated with the substitution of atoms in the PbZr0.53Ti0.47O3 lattice by atoms in the Mn0.4Zn0.6Fe2O4 lattice during the high‐temperature sintering of composite samples. A correlation is revealed between the transverse magnetoelectric voltage coefficient and smearing parameters of the ferroelastic phase transition.