To study the behaviour of a haemocyte when crossing a stenotic capillary, the immersed boundary-lattice Boltzmann method was used to establish a quantitative analysis model. The haemocyte was assumed to be spherical and to have an elastic cell membrane, which can be driven by blood flow to adopt a highly deformable character. In the stenotic capillary, the spherical blood cell was stressed both by the flow and the wall dimension, and the cell shape was forced to be stretched to cross the stenosis. Our simulation investigated the haemocyte crossing process in detail. The velocity and pressure were anatomised to obtain information on how blood flows through a capillary and to estimate the degree of cell damage caused by excessive pressure. Quantitative velocity analysis results demonstrated that a large haemocyte crossing a small stenosis would have a noticeable effect on blood flow, while quantitative pressure distribution analysis results indicated that the crossing process would produce a special pressure distribution in the cell interior and to some extent a sudden change between the cell interior and the surrounding plasma.