A three-dimensional field solution is presented foraxially polarized permanent magnet cylinders. The fieldcomponents are expressed in terms of finite sums of elementaryfunctions and are easily programmable. They can be used todetermine the operating point of rare-earth magnet cylinders.They are also useful for performing rapid parametriccalculations of field strength as a function of materialproperties and dimensions. The field components aredeveloped for different magnet arrangements by taking intoaccount the back iron. Also the method of images is used. Usingthe field equations, three-dimensional analytical expressionsare derived for computing the magnetic force between axiallypolarized permanent-magnet cylinders for different magneticarrangements. The field calculated results are in goodagreement with the experimental data.