Elastic modulus in fluid is a crucial thermodynamic property due to its close relation to the viscoelastic behaviors in dynamics and the pore size analysis in porous materials. Especially, elasticity in nanoconfined fluid, which exhibits significant deviation from that of bulk fluid, has gained a multitude of applications in industrial and engineering fields. In this work, general expressions of bulk and shear moduli for inhomogeneous fluids have been derived based on Hooke's law. In the bulk phase, the obtained moduli reduce exactly to those obtained from thermodynamic fluctuation theory. In addition, both moduli have been expressed as functionals of fluid density functions. Besides, the Cauchy relation and Voigt notation for inhomogeneous elasticity have been first obtained. The validity of the obtained moduli has been verified through their comparison with grand canonical Monte Carlo simulation. Our further calculations suggest that the bulk modulus of confined fluid is inhomogeneous across the pore and the averaged bulk modulus is significantly enhanced by the confinement. In addition, the pore size dependence of the bulk modulus and the related Tait-Murnaghan equation have also been investigated in confined argon. It is found that in small pores, the modulus and Tait-Murnaghan equation show obvious oscillation with pore size. For larger pores, however, these properties reduce linearly to the values in the bulk case.