This paper presents an analytical model for 3D airgap slotless Halbach permanent magnet synchronous machines which utilize both radial and axial airgaps. The proposed model estimates the permanent magnet flux linkage and inductance by combining magnetic fields predicted from the four 2D subdomain models for the radial flux main, radial flux overhang, axial flux main, and axial flux overhang segments expressed in terms of Fourier series. For the overhang segments, multi-slice technique is used to predict the flux linkages for the round corner of the coils. The end effect leakage compensation method for the axial flux segments is derived from a magnetic equivalent circuit model and the end winding inductance is calculated analytically. The proposed model can predict permanent magnet flux linkage and inductance of the 3D airgap slotless machines within 3 percent error range compared to the 3D finite element method model at one order of magnitude less computational time.