The elastic and thermal properties of Sr1-xYxCoO3 (0 <= x <= 0.5) have been investigated, probably for the first time, by using modified rigid ion model. We present the elastic constants (C-11,C- C-12 C-,(44)) and other elastic properties like bulk modulus (B), Young's modulus (Y), shear modulus (G), Poisson's ratio (sigma), Lame's parameter (mu, lambda ), transverse, longitudinal and average wave velocity (upsilon(t,)upsilon(l) and upsilon(m)) and anisotropy parameter (A). Besides, we have reported the thermodynamic properties molecular force constant (f), Reststrahlen frequency (upsilon), cohesive energy (phi), Debye temperature (theta(D)) and Gruneisen parameter (gamma). We have also computed the variation of specific heat (C) and volume thermal expansion coefficient (alpha). The computed results on the elastic and thermodynamic properties are the first report on them. This model is capable of explaining the Cauchy's discrepancy, elastic and thermal properties successfully.