In this paper, we propose a technique for the prediction of s-wave velocity in carbonate formations with different types of secondary porosity using conventional logs (p-wave slowness, micro-resistivity, total porosity and density). The technique consists of the determination of the pore microstructure parameters (matrix and secondary porosities, shapes of the secondary pores) using the joint petrophysical inversion of well logs and simulation of the s-wave log for the medium with obtained characteristics. In the inversion procedure, the calculation of the theoretical logs is based on the model of a double-porosity medium that consists of a homogeneous isotropic matrix with a primary pore system and secondary pores approximated by spheroidal inclusions placed in the matrix. Selecting the aspect ratio of inclusions we have simulated different types of secondary porosity such as vugs (close to spherical inclusions), vugs connected by channels (prolate spheroids) and cracks (flattened spheroids). We have applied the self-consistent method (the effective medium approximation) to simulate physical properties including the s-wave slowness from the double-porosity model. The technique has been verified using a theoretical model and experimental data from the South Zone of Mexico. The results of this technique application have demonstrated a good agreement between measured and reconstructed s-wave logs in carbonate formations.