We investigate structural, kinematic and chemical properties of stars and gas in the Small Magellanic Cloud (SMC) interacting with the Large Magellanic Cloud (LMC) and the Galaxy based on a series of self-consistent chemodynamical simulations. We adopt a new ‘dwarf spheroidal model’ in which the SMC initially has both old stars with a spherical spatial distribution and an extended Hi gas disk. We mainly investigate the evolution of the SMC for the last ∼3 Gyr, during which the Magellanic Stream (MS) and the Magellanic Bridge (MB) could have formed as a result of the LMC–SMC–Galaxy interaction. Our principal results, which can be tested against observations, are as follows: The final spatial distribution of the old stars projected onto the sky is spherical, even after strong LMC–SMC–Galaxy interaction, whereas that of the new ones is significantly flattened and appears to form a bar structure. Old stars have a line-of-sight velocity dispersion σ ≃ 30 km s−1 and slow rotation, with a maximum rotational velocity, V < 20 km s−1 and show asymmetry in the radial profiles. New stars have a smaller Σ than old ones and a significant amount of rotation (V/σ > 1). Hi gas shows velocity dispersions of σ = 10–40 km s−1, a high maximum rotational velocity (V ∼ 50 km s−1) and a spatial distribution similar to that of new stars. New stars with ages younger than 3 Gyr show a negative metallicity gradient in the sense that more metal-rich stars are located in the inner regions of the SMC. The MB inevitably contains old stars with surface mass densities of 6−300 × 104 M⊙ deg−2 depending on initial stellar distributions of the modeled SMC. We find that the dwarf spheroidal model can explain more self-consistently the observed kinematic properties of stars and gas, compared with another type of the model (‘the disk model’) in which the SMC initially consists of stellar and gas disks. We suggest that, to better understand its evolution, the SMC needs to be modeled as having a spheroidal component, rather than being a pure disk.