Measurements of Young’s modulus and thermal expansion at −150°∼400°C and of rigidity modulus and hardness at room temperature have been carried out with Mn–Cu alloys subjected to a variety of heat treatment and cold-working. It is shown that Mn–Cu alloys containing 6.00∼57.46% Cu slow-cooled after heating for 1 hr at temperatures 80°C below the melting points have distinct anomalies in Young’s modulus-temperature curves, revealing the Elinvar property. The anomalies are considered to be due to the antiferromagnetism of the γ phase. The values of Young’s modulus in the annealed state are higher than those in the cold-worked or the water-quenched state, the difference being remarkably large in the (α+γ) phase on the Mn side. The hardness of Mn-13∼17% Cu alloys is very high regardless of the heat treatments involved. The temperature coefficient of Young’s modulus undergoes a wide variation with annealing, water-quenching, cold-working and reheating after water-quenching or cold-working, and also with alloy composition. It is also noted that the temperature coefficients of Young’s modulus as a function of composition exhibit large maxima and minima in positive and negative signs, thus showing the Elinvar property. The highest positive temperature coefficient of Young’s modulus in the annealed state is +14.7×10⁻⁵ for the alloy containing 56.40% Cu. Further, the variation in rigidity modulus and its temperature coefficient with heat treatment, cold-working and composition bears a close resemblance to that in Young’s modulus and its temperature coefficient.