The mechanical properties of a ceramic superconductor material (YBaCuO or Y-123) have been studied using the Nanoindentation technique, for Bridgman and Top Seeded Melt Growth textured samples. The structure of the textured material is heterogeneous, and two different phases are present: a matrix of Y-123 and Y-211 spherical or quasi-spherical inclusions. The Hardness and Young's modulus have been obtained for each phase using a sharp tip indenter and the Oliver and Pharr equations. The different fracture mechanisms activated around and under the residual imprints have been observed by Scanning Electron Microscopy and Focused Ion Beam, respectively. The elastic-to-plastic transition has been studied using the Hertz equations and a spherical tip indenter, thus obtaining the yield strength, the shear stress and the stress-strain curves for each texture process. Finally, the different plastic deformation systems (dislocations, and twinning processes) activated during the elastic to elasto-plastic transition have been studied and observed using the Atomic Force Microscopy.