Fig. 7a shows typical hysteresis loops for the axial levitation force between the permanent magnet and the Y123 superconductor. For the zero-field-cooled (ZFC) process, the maximum and repulsive force value is obtained at zero separation distance. The force can be written as F = m(dH/dx), where m is the magnetic moment related with magnetization M and volume of the superconductor and dH/dx is a field gradient produced by the magnet. Due to the magnetic stress between trapped field in the sample and the permanent magnet, an attractive force occurs when the sample is moved away from the magnet. The undoped YBCO sample showed maximum repulsive force. Increasing the Ti concentration leads to a reduction in the repulsive force. This result can be attributed to the number of pinning centers increased by increasing Ti content in sample which results to the increase of trapped magnetic field inside the samples. In addition, levitation force is a function of the grain size and crystallographic orientation. As presented in Fig. 2, the grain size decreased with increasing TiO2 content. It can be also seen that the crystallographic orientation of samples is changed with increasing TiO2 content. The zero-distance levitation force density ( F0) values and the difference of repulsive force (Fr) and attrac- tive force (Fa) at 3 mm from the permanent magnet for Ti-doped YBCO samples are shown in Fig. 7b. It was found that the zero-distance levitation force values decrease slightly with increasing Ti content up to 5 wt.%. For 7 and 10 wt.% Ti-doped samples, a small increase is found. The changes in levitation force are related to the change of the grain size and orientation in samples. In addition, the weak-links and cracks present in samples result in a small levitation force [3].