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[Biscaynes]

Here is the trick: Go to pec (playstation emulator cheater) and add following code for Driver version 1.1: 8009683C 0002 or 800964FC 0002 for version 1.0. It's car modifier code. When you normally send it to plugin when you're in the main menu, it will change your car to secret one. Don't do it, just activate it after the loading time when you are on the road. It also works on PSP with cwcheat. Of course you can use secret car like I did in my vid in NY, but then change 0002 to 0003 for example and activate code again.
To change your car replace 'XX' with the number in the table below for relevant car and activate the code before you enter any driving mode.
+-------------------------------+-------­------------------------+
MIAMI
+-------------------------------+-------­------------------------+
| 00 | Chevrolet Chevelle
| 01 | Buick Regal
| 02 | White Car (?)
| 03 | Ford Mustang Mach One
+-------------------------------+-------­------------------------+
SAN FRANCISCO
+-------------------------------+-------­------------------------+
| 00 | Dodge Charger
| 01 | Taxi
| 02 | Chevrolet S-10 (truck)
| 03 | Tan Car (?)
+-------------------------------+-------­------------------------+
LOS ANGELES
+-------------------------------+-------­------------------------+
| 00 | Buick Skylark
| 01 | Brown Car (?)
| 02 | Police Car
| 03 | Creme Car (?)
+-------------------------------+-------­------------------------+
NEW YORK
+-------------------------------+-------­------------------------+
| 00 | Ford Gran Torino
| 01 | Taxi
| 02 | Police Car
| 03 | Chevrolet Nova
| 04 | Cadillac Limousine
+-------------------------------+-------­------------------------+
DIRT TRACK
+-------------------------------+-------­------------------------+
| 00 | Chevrolet Chevelle
| 01 | Invisible Car *(1)
+-------------------------------+-------­------------------------+
CAR PARK
+-------------------------------+-------­------------------------+
| 00 | Chevrolet Chevelle
| 01 | Invisible Car *(2)

Games that have a very similar damage model:

- Super Runabout San Francisco Edition (Sega Dreamcast) Release date: 2000

- Crashday

Note:
Police car & taxi in NY have real time damage by default. Don't use the trick, start crashing heavilly and you'll see real time deformation!

[RacingFreak]

Is it me, or that damage cheat acts as our modified car models (on PC) with damage turned on?

[Fireboyd78]

Is it me, or that damage cheat acts as our modified car models (on PC) with damage turned on?

Yep, because when you do this cheat, you're changing the car model Driver is processing, so therefore, it's trying to access a non-existent damage model, which in turn gives you this "real time damage effect"

It's a glitch, lol.

[Clutch]

Except textures glitch it is very nice glitch overall