A self-consistent field theory is used to predict structural, mechanical, and thermodynamical properties of linear micelles of selected nonionic surfactants of the type C(n)()E(m). Upon increase in surfactant concentration the sudden micelle shape transition from spherical to cylindrical (second critical micelle concentration (cmc)) is analyzed. The cylindrical micelles consist of a body (with radius R(c) and length L) and two slightly swollen endcaps. For small L, the shape resembles a dumbbell. With increase in the length of the body, an oscillatory behavior in the grand potential of the micelle is found. The wavelength of the oscillation (lambda(d)) is proportional to the surfactant tail length n. The amplitude of these oscillations decreases exponentially with a decay length xi. In the limit of very long micelles, the grand potential converges to the endcap (free) energy E(c). This endcap energy increases approximately quadratic with the tail length and diminishes by increasing the headgroup size m. The micelle size distribution is generated showing non-monotonic features due to the presence of short dumbbells and becomes exponential when L >> 8R(c). It is also shown that the endcap energy can be estimated in first order by the grand potential of the spherical micelle that coexists with infinitely long cylindrical micelles. The persistence length l(p) of these linear micelles is evaluated to estimate the relative importance of conformational entropy for these micelles.