• Chevrolet?
Some people apparently agree with the Pixarcars wiki saying Matter is a "a 1951 International Harvest (sic) L-170 truck with elements of a mid-1950s Chevrolet". As I'm not the only one to use pictures related search engines, I wonder how such a joke (it is one, isn't it?) can go on:

(1955 Chevrolet 4100 Tow truck vs. "disguised" -1951 ?-International Harvester L-170 one

For me, Mater is more likely a kind of squeezed Chevrolet, but not an International Harvester. Even with make-up. And even more when it recovers its hood.

(01:46:23 - End credits)

For the record, there are a lot of contenders for Mater's origin:

And so on...

• 3800 or..?
It has dual rear wheels, so it can't indeed be less than a ¾-ton 3800 model. Smaller models were made on pickup basis, anyway, as already seen in the IMCDb. But 3800, 4100 and 6100 trucks had almost the same wheelbase: 135" / 3.43 m for the 3800, shorter 130" / 3.30 for the 2 medium-duty trucks. So the wheelbase is not the clue that may show the difference:

(1955-56 3800 tow truck // 1955 4100 wrecker // 1957 6100 model)

Yet, as I see it, Mater seems indeed not to have the 3800 model small (5" / 13 cm?) body part between the wheel arch and the door, looking then more like a medium-duty truck. Provided that the cartoonists tried to stick more or less close to the reality...

The grille is not visible, so only the wheel rims remain: on light-duty 3800 models, they have numerous holes (8 to 9), but medium- and heavy-duty trucks wheel rims have only a few of them (5 to 6):

(3800 model - Here is another one // medium-duty model)

As almost all pictures show Mater with 4- to 5-hole wheel rims, and