This article uses a fully quantitative approach to describe the behavior of the minute tip of the magnetic force microscope (MFM) over longitudinally directed magnetic bits. Three possible magnetic structures are taken into consideration together with a realistic tip model. The magnetic and van der Waals interactions beween the tip and the sample are derived analytically to simulate a force gradient in MFM. The contours of the constant force gradient are presented and related to the known experimental data. The important role of the van der Waals force gradient in constant force gradient measurements is shown. The force gradient from a magnetic interaction is partly negative and partly positive and is balanced or increased by the (always positive) van der Waals force gradient. Force gradient asymmetry above the transition area is revealed when the MFM tip is tilted. By tilting the tip, the detection of two components of a stray field is accomplished. We found that the widths and heights of observed bumps of a force gradient depend on the width of the transition area and the deviation of the magnetization vector from the recording direction. These factors are especially important in determining what tolerance can be put on a read/write head’s performance. A lateral resolution of 90 nm could be achieved with our tip model.