For the first three episodes, Tom Mason (Noah Wyle) is seen carrying a Norinco Type 56-1, the Chinese underfolding stock copy of the AKMS, with its distinctive hooded front sight. The rifle also appears to have duct tape wrapped around the end of the stock, presumably for relief when the rifle is put to the shoulder.
Norinco Type 56
Several resistance fighters are seen armed with Norinco Type 56 rifles.
AKM
Throughout the remainder of Season 1, Tom Mason (Noah Wyle) carries an AKM as his preferred weapon.
After having lost his M4A1 during the events of Episode 3, Hal Mason (Drew Roy) carries a Galil MAR carbine fitted with a conventional bolt handle and top mounted rail as his preferred weapon.
M4A1 Carbine
Colt M4A1 carbine is a prominent weapon seen carried by the resistance. In the first episodes, Hal Mason (Drew Roy) is seen carrying the M4A1. Jimmy Boland (Dylan Authors) carries his M4A1 fitted with an EOTech sight.
M16A1
An M16A1 can be seen in the hands of a resistance fighter.
M16A2
Several resistance fighters are seen armed with M16A2 rifles.
M16A4
One resistance fighter can be seen armed with an M16A4 rifle, identifiable by the removable carry handle/rear sights.
A rifle of the Heckler & Koch pattern can be seen being used by one of Pope's gang in "The Armory" (S1E02). It is possible that this is the civilian version of the Heckler & Koch G3, the HK91, as noted by the lack of the grenade launching lug on the barrel. It also appears to have a flashlight attached to side of the front sight block.
L1A1 SLR
The British variant of the FN FAL rifle, the L1A1 SLR is seen in the hands of of a resistance fighter inside a grocery store.
Rifles
M1 Garand
An M1 Garand can be seen on the right of this promotional image with the butt rested on the ground.
Marlin Model 336
A Marlin Model 336 can be seen in the hands of one of the resistance fighters.
Sonya, a woman that Tom, Hal, and Weaver encounter in Boston, fires on the group with a Karabiner 98k, an interesting choice for a survivor of the attack. Note The weapon has a hooded front sight, indicating that it is of late to post war manufacture.
Springfield Armory M1A
One of Terry Clayton's men in "Sanctuary (Part 2)" carries a M1A Rifle. John Pope later takes the rifle and uses it in a shoot out with Clayton's men.
A variant of the Colt M1911A1 is carried by Maggie (Sarah Carter). The pistol is fitted with ivory grips and is first seen in "The Armory" (S1E02). She is seen to carry 2 of theses in a black leather shoulder rig.
Colt Single Action Army
John Pope (Colin Cunningham) is seen carrying a Colt Single Action Army as his sidearm, notably in "The Armory" (S1E02). In (S1E08), he uses his SAA to test out a new armor-piercing round.
At the beginning of the premiere episode "Live and Learn" (S1E01), a Remington 870 shotgun with an extended mag tube is seen used by a resistance fighter at a human checkpoint.
Mossberg 590a1 Special Purpose
A Mossberg 590 is used by Weaver in Episode 6 to dispatch a skitter on route to kill/capture Jimmy. The 8-shot is parkerized with ghost-ring sites; whether or not the Speedfeed is present, cannot be seen.
Machine Guns
Browning M2HB
A Browning M2HB is the main heavy weapon used by the 2nd Massachusetts in Season 1. The machine gun is mounted in a Pontiac GTO.
FN M240B
The M240B is another weapon used by the 2nd Massachusetts. It's first seen being carried by Anthony (Mpho Koaho) in the series premiere "Live and Learn" (S1E01). Tom Mason (Noah Wyle) can be seen firing an M240B when his squad ambushes Pope's bandits in "The Armory" (S1E02). The Falling Skies website mistakenly refers to this machine gun as a .50 Caliber weapon, when, in fact, it uses the .308 Winchester round.
PKM
A PKM machine gun is seen being fired by Hal Mason (Drew Roy) when the squad ambushes Pope's gang at the end of "The Armory" (S1E02).
RPK
An RPK machine gun is seen being fired by Anthony (Mpho Koaho) when the squad ambushes Pope's gang at the end of "The Armory" (S1E02).
Tom Mason (Noah Wyle) can be seen firing an RPG-7. The Falling Skies website erroneously refers to it as a "Bazooka", a completely different weapon system.
Other Weapons
Molotov Cocktail
Tom Mason (Noah Wyle) fashions a molotov cocktail to distract several gun-wielding "harness" kids, when surrounded in the motorcycle store.