In this paper, the size-dependent shear deformable conical shell formulation is derived based on the modified couple stress theory and first order shear deformation model to investigate the free vibration of functionally graded conical shell embedded in an elastic Pasternak medium and subjected to thermal environment. The material properties are considered temperature-dependent and graded in thickness direction according to power law distribution. The governing equations and boundary conditions are derived using Hamilton’s principle. The size effect is taken into account using the modified couple stress theory, and, the free vibration of simply supported FG truncated conical nanoshell is investigated as a special case. The effects of different parameters such as dimensionless length scale parameter, temperature change and distribution of the nanoshell components on the natural frequency are investigated based on the modified couple stress theory and classical continuum theory.