Linear Flux Switching Machines (LFSMs) are suitable candidates for long stroke applications as they confines all excitation sources to primary thus leaving completely passive, robust, and low cost secondary. Permanent Magnet LFSMs (PMLFSMs) enables high thrust force density and efficiency. However, deficiency of controllable air-gap flux, risk of PM demagnetization, and increasing cost of rare earth PM materials diverted researchers towards Field Excited LFSMs (FELFSMs). FELFSMs wiped out aforementioned PMLFSM's shortcomings at the cost of low thrust force density. In this paper, merits of PMLFSM and FELFSM are combined by proposing a novel Hybrid Excited LFSM (HELFSM). Proposed machine is excited by PMs, Field Excitation Coils (FECs), and Armature Windings (AWs). However, complex magnetic circuit of poly-excited HELFSM compels designers to adopt FE Analysis (FEA) for design, analysis, and optimization. To decrease dependency on computationally complex and time consuming FEA, an analytical model combining lumped parameter magnetic equivalent circuit, Fourier analysis, Laplace equation, and Maxwell Stress Tensor method is proposed to predict open-circuit flux linkage, B-EMF, normal and tangential components of no-load and on-load magnetic flux density, detent, and thrust force performance. Finally, predictions of the developed analytical model are validated with corresponding FEA and experimental results.INDEX TERMS Analytical modeling, finite element analysis, hybrid excited linear flux switching machine, lumped parameter magnetic equivalent circuits, maxwell stress tensor, segmented secondary.