Fe-Ni alloys can have a variety of magnetomechanical properties, depending on their composition. In order to study the magnetoelastic coupling of the alloys, we obtained the stress dependence of the longitudinal and transverse magnetostriction curves and three magnetoacoustic curves, i.e., the speeds of a longitudinal and two transverse waves propagating in a normal direction to the magnetic field. We obtained five curves, each for Ni, B-type Permalloy, and pure iron under tensile stresses from 0 to 40 MPa parallel to the magnetic field. It is known that the magnetoelastic coupling and the acoustoelasticity induce a uniaxial anisotropy in the elastic coefficients of the ferromagnetic materials. We propose a procedure to determine all the elastic coefficients from the above five curves. We also examine the variation of the elastic coefficients with magnetization by taking into account their stress dependence and comparing them with Fe-Ni alloys .