New high resolution spectroscopic and medium resolution spectropolarimetric data, complemented with optical broad and narrow band imaging, of the B[e] star HD 87643 are presented. The spectrum of HD 87643 exhibits the hybrid characteristics well known to be representative of the group of B[e] stars; a fast wind with an expansion velocity in excess of 1000 km/s is measured in the hydrogen and helium lines, while a slower component is traced by lower excitation lines and forbidden lines. Clues to the geometry of the rapidly expanding circumstellar shell are provided by the startling polarization changes across Halpha. Comparison with published schematic calculations indicates that the polarizing material is located in a slowly rotating, expanding disk structure. A hydrodynamical model is then presented whose results are consistent with the original two-wind concept for B[e] stars and exhibits kinematic properties that may well explain the observed spectral features in HD 87643. The model calculations use as input a B star undergoing mass loss, surrounded by an optically thick disk. The resulting configuration consists of a fast polar wind from the star and a slowly expanding disk wind. The model also predicts that the stellar wind at intermediate latitudes is slower and denser than in the polar region.