A method measuring elastic properties using ultrasound of a part made of a material having a curved surface, includes: emission of bundles of ultrasound waves in a direction of a point of impact on the part's surface to generate waves within the part; knowing a thickness d of the part at the point of impact in a first direction D1 and a thickness d2 in a second direction forming an angle determined with respect to the first direction, taking a first measurement t1 of time taken by the longitudinal waves transmitted to travel d1 from the point of impact, and taking a second measurement t2 of the time taken by the transverse waves to travel d2 from the point of impact; and determining the Young's modulus and/or Poisson's ratio of the material based on the longitudinal velocity VL=d1/t1 and transverse velocity VT=d2/t.