This study aimed to evaluate the ability of the response surface methodology (RSM) approach to predict the tractive performance of an agricultural tractor during semi-deep tillage operations. The studied parameters of tractor performance, including slippage (S), drawbar power (DP) and traction efficiency (TE), were affected by two different types of tillage tool (paraplow and subsoiler), three different levels of operating depth (30, 40 and 50 cm), and four different levels of forward speed (1.8, 2.3, 2.9 and 3.5 km h􀀀1). Tractors drove a vertical load at two levels (225 kg and no weight) in four replications, forming a total of 192 datapoints. Field test results showed that all variables except vertical load, and different combinations of this and other variables, were effective for the S, DP and TE. Increments in speed and depth resulted in an increase and decrease in S and TE, respectively. Additionally, the RSM approach displayed changes in slippage, drawbar power and traction efficiency, resulting from alterations in tine type, depth, speed and vertical load at 3D views, with high accuracy due to the graph’s surfaces, with many small pixels. The RSM model predicted the slippage as 6.75%, drawbar power as 2.23 kW and traction efficiency as 82.91% at the optimal state for the paraplow tine, with an operating depth of 30 cm, forward speed of 2.07 km h􀀀1 and a vertical load of 0.01 kg.