An analyzing mesh generating apparatus has a model read unit for reading data, a required quality and shape data of an input hexahedral mesh model, a display unit for displaying said hexahedral mesh model, and a mesh element number reduction unit for reducing the number of mesh elements in the data. The analyzing mesh generating apparatus has also a mesh quality evaluation unit for evaluating a mesh quality regarding whether mesh element reduction is performed while maintaining the required quality data, and a mesh fine division unit for performing mesh fine division to change meshes to coarse/dense meshes, relative to the hexahedral mesh model with the reduced number of mesh elements in the data.