A code is developed using the hybrid Cartesian/immersed boundary method and it is applied to simulate flows around a three-dimensional deforming body. A new criterion is suggested to distribute the immersed boundary nodes based on edges crossing a body boundary. Velocities are reconstructed at the immersed boundary nodes using the interpolation along a local normal line to the boundary. Reconstruction of the pressure at the immersed boundary node is avoided using the hybrid staggered/non-staggered grid method. The developed code is validated through comparisons with other experimental and numerical results for the velocity profiles around a circular cylinder under the forced in-line oscillation and the pressure coefficient distribution on a sphere. The code is applied to simulate the flow fields around a plate whose tail is periodically flapping under a translation. The effects of the velocity and acceleration due to the deformation on the periodic shedding of pairs of tip vortices are investigated.