Motivated by the application of Winkler-like models for the buckling analysis of embedded carbon nanotubes, an orthotropic Winkler-like model is developed to study the buckling behavior of embedded cytoskeletal microtubules within the cytoplasm. Experimental observations of the buckling of embedded cytoskeletal microtubules reveal that embedded microtubules bear a large compressive force as compared with free microtubules. The present theoretical model predicts that embedded microtubules in an elastic medium bear large compressive forces than free microtubules. The estimated critical pressure is in good agreement with the experimental values of the pressure-induced buckling of microtubules. Moreover, due to the mechanical coupling of microtubules with the surrounding elastic medium, the critical buckling force is increased considerably, which well explains the theory that the mechanical coupling of microtubules with an elastic medium increases compressive forces that microtubules can sustain. The model presented in the paper is a good approximation for the buckling analysis of embedded microtubules.