Neutron scattering and ultrasonic methods have been used to study the lattice dynamics of two single crystals of Ni-Mn-In Heusler alloys close to Ni₅₀Mn₃₄In₁₆ magnetic superelastic composition. The paper reports on the experimental determination of the low-lying phonon-dispersion curves and the elastic constants for this alloy system. We found that the frequencies of the TA₂ branch are relatively low and it exhibits a small dip anomaly at a wave number ξ₀≈1/3, which softens with decreasing temperature. Associated with the softening of this phonon, we also observed the softening of the shear elastic constant C′=(C₁₁−C₁₂)/2. Both temperature softenings are typical for bcc-based solids which undergo martensitic transformations and reflect the dynamical instability of the cubic lattice against shearing of {110} planes along ⟨11̅ 0⟩ directions. Additionally, we measured low-lying phonon-dispersion branches and elastic constants in applied magnetic fields aimed to characterize the magnetoelastic coupling.