A sample of six SMC cool stars (K supergiants) are analysed by high resolution spectroscopy in order to investigate their chemical content, which should reflect that of the current interstellar medium within the SMC. The abundance of Na, Al, {alpha}-elements, Fe peak and heavy elements are derived through an LTE analysis of the lines, compared to a Galactic "standard" (the well-studied K giant Arcturus) and discussed in terms of chemical evolution of the SMC. The following results were obtained: 1. All the stars from this sample are metal deficient ([Fe/H] ranges from -0.59 to -0.89dex). The abundance varies little from star-to-star (0.10dex rms, comparable with the expected error due to uncertainties on the effective parameters of the stars), in agreement with the very small chemical composition variations among the H II regions within the SMC found by Pagel et al. (1978MNRAS.184..569P). 2. Sodium is not strongly enhanced in these stars, and the star-to-star scatter is larger than expected. 3. At variance with metal-poor stars in our Galaxy, the so-called {alpha}-elements do not seem to be enhanced. 4. Nickel displays a noticeable depletion with respect to iron ([Ni/Fe]=~-0.3dex), at variance with what is found in the SMC F supergiants and in Arcturus. 5. Except for PMMR 144, the s and r process elements heavier than Ba are enhanced in all of our stars by =~+0.4dex.