In this paper, we present a new tubular permanent-magnet linear machine with square-shaped cross section and derive its corresponding analytical model by solving Maxwell equations and applying the superposition theorem. The analytical field solution is necessary for obtaining an analytic form of the machine parameters and variables such as the self- and mutual inductances of the windings, the thrust force, and the windings electromotive force (EMF). These provide a valuable tool for tubular machine analysis, design, and optimization. In order to achieve maximum force density, we optimized the design parameters of the proposed machine using the analytical model. We used finite-element analysis and experimental results to demonstrate the validity of the developed analytical model. Again using the Fourier series of the cogging force and its harmonic analysis, in this paper, we introduce two techniques for cogging force reduction in the new tubular linear permanent-magnet machine. The first technique reduces the cogging force due to interaction between the permanent magnets and the stator teeth, and the other reduces the cogging force due to finite length of the armature. These techniques are straightforward, and their implementations in the tubular linear permanent magnet machine with square cross section are easy. We investigated the effectiveness of the proposed techniques in cogging force reduction by 3-D finite-element analysis and experimental measurements.