To unlock these cars you must meet the criteria shown below.

Mitsubishi Lancer EVO 4 - Finish 1st in the 2nd Year Regular Mode.
Toyota Celica GT-Four ST-185 - Finish 1st in the 3rd Year Regular Mode.
Mitsubishi Lancer EVO 3 - Finish 1st in the 4th Year Regular Mode.
Peugeot 106 Maxi - Finish 1st in the 5th Year Regular Mode.
Lancia Delta Integrale - Finish 1st in the 6th Year Regular Mode.
Fiat 131 Abarth - Finish 1st in the 7th Year Regular Mode.
Peugeot 205 Turbo - Finish 1st in the 8th Year Regular Mode.
Renault Alpine A110 - Finish 1st in the 9th Year Regular Mode.
LANCIA 037 Rally - Finish 1st in the 10th Year Regular Mode.