Background. The purpose of this study was to determine if energy cost of walking ((V) over dot O-2) could be accurately predicted with the simple models which analyze relationship oxygen uptake-speed of walking. A model to predict energy cost of treadmill walking was published firstly 29 years ago. Methods. Employing the new modification of this model from 1986 to analyze (V) over dot O-2 -speed of walking relationship leads to the elaboration of a simple linear model, two-compartment linear model, polynomial model of second order and monoexponential model of the metabolic cost of treadmill walking. To verify and compare these models 87 males, age ranged from 19 to 62 years, were evaluated on a motor driven treadmill. They walked at 0% grade at various velocities ranged from 3 to 12 km.h(-1). Results. The linear model has in range of intensities 3-12 km.h(-1) a form of (V) over dot O-2 . kg(-1) (ml.kg(-1).min(-1))=5.228*v (km.h(-1))-11.158, r=0.812, S-EE=4.16 ml.kg(-1).min(-1). The two-compartment linear model has in range of intensities of 3-7 km.h(-1) a form of (V) over dot O-2 . kg(-1)=3.207*v(km.h(-1))-1.777, r=0.932, and S-EE=1.5. In the range of 7.1-12 km .(V) over dot O-2 kg(-1)=7.120*v-29.168, r=0.901, S-EE=3.78. In the range of intensities from 3 to 12 km.h(-1) a polynomial model was found in the form (V) over dot O-2.kg(-1) =4.501-0.108*v+0.379*v(2), r=0.891, S-EE=4.43, and the exponential model had a form (V) over dot O-2 . kg(-1)=4.360*exp(0.223*v), r=0.861, S-EE=6.84. All these correlation coefficients were highly significant (p<0.001 in all cases). Conclusions. It was concluded that when applied to adult population, the models provide reasonable estimate of the actual requirement for treadmill walking provided the subjects in a oxygen uptake steady-state. As other researches for (V) over dot O-2/step we have found U-shaped curves of coefficient energy cost of walking. The minimum was at speed about 4 km.h(-1). This finding support the speculation that does exists the ''optimal'' speed of moving which reflects the minimal energy expenditure during the walking.