The potential use of sugar beet shreds for copper ions removal from aqueous solution in a fixed-bed column was investigated. Experiments were performed using Box-Behnken experimental design on three levels and three variables: concentration of the inlet solution (50-150 mg L-1), adsorbent dosage (8-12 g) and pH of the inlet solution (4.0-5.0). The obtained breakthrough curves were fitted with two common empirical models, Bohart-Adams and dose-response. Observing the asymmetric shape of the breakthrough curves, the new mathematical model was proposed. The new model proposes the breakthrough curve composed of two parts, sum of which gives the asymmetrical S-shaped curve, accurately matching experimental data. Regarding the lowest SSer (7.8.10(-4)) and highest R-2 (0.9998), new model exhibited the best fit comparing to the commonly used models. RSM and ANN modelling were employed for process variables evaluation and optimization. The most influential parameter exhibiting negative influence on target response (critical time) was concentration of the inlet solution, while the adsorbent dosage exhibited positive influence. Optimization procedure revealed that the highest critical time (341.4 min) was achieved at following conditions: C-0 = 50 mg.L-1, m(a) = 12 g and pH 4.53 by ANN, while RSM considered pH as insignificant factor and obtained 314.8 min as the highest response.