At request of the short-lived Democratic Republic of Georgia he moved back to his native country in 1920 in order to organize the establishment of a national scientific school.

From 1956 to 1976 Muskhelishvili was chairman of the National Committee of the USSR on Theoretical and Applied Mechanics (established by the Decree of the Presidium of the Academy of Sciences).

Muskhelishvili conducted fundamental research on the theories of physical elasticity, Integral equations, Boundary value problems and other.

He is also credited with major contributions to the theory of linear boundary value problems for analytic functions and one-dimensional integral equations.

During World War II Muskhelishvili was responsible for retargeting the preoccupation of the Academy of Science to national defense.

He completed a series of research, experimental and theoretical work in different areas of applied mathematics, physics and mechanics, which all had great practical importance and decisive impact on the development of a range of military hardware during and after the war.

Muskhelishvili was a renowned specialist in engineering able to apply a lot of his theories and solutions, including torsion bar suspension for tracked vehicles such as tanks.