• Probably the first report on the specific heat in Ln 0.05 Sr 0.95 CoO 3− δ (A = Sm, Gd, Dy, Y, Ho, Er, Tm and Yb). • The second-order elastic constants (SOECs) have been reported by us for the first time. • The computed values of elastic constants shows that Ln 0.05 Sr 0.95 CoO 3− δ (A = Sm, Gd, Dy, Y, Ho, Er, Tm and Yb) these compounds are mechanically stable and obey to stability criteria. • The negative values of cohesive energy show the stability of these compounds. The elastic and thermal properties of highly Sr-doped Ln 0.05 Sr 0.95 CoO 3− δ (Ln = Sm, Gd, Dy, Y, Ho, Er, Tm and Yb) in cubic phase have been investigated probably for the first time by using modified rigid ion model (MRIM). The computed results on the second order elastic constants ( C 11 , C 12 and C 44 ) and their combinations are reported and discussed. The calculated elastic constants indicated that Ln 0.05 Sr 0.95 CoO 3− δ are mechanically stable. Besides, we have reported the cohesive, thermal properties and the variations of specific heat with temperature are discussed in detail.