The present paper describes our experience with the parallelization of the pseudo-spectral computer code FLOWH, which is used for DNS simulations of the channel and flume flows. The original version of the FLOWH code was developed by Gavrilakis et al. 1986  and was optimized for vector computers (Cray...). In 1999 and 2000 we started the parallelization of the code for the shared memory type of parallel computers SGI Origin and Sun for turbulent heat transfer calculations (Tiselj et. al. [1,2]). OpenMP parallelization directives were used and very similar performances were obtained on both types of computers. The efficiency of the parallelization on 32 CPUs is approximately 50%. The main reason for the relatively low efficiency of the parallelization (comparing to the efficiency of finite volume codes) is in the nature of the pseudo-spectral codes, which does not allow permanent allocation of the nodes onto the particular CPU like finite volume or finite element codes.