Officers are appealing for information after the "cash in transit" incidents, which on both occasions left the culprits empty-handed, on Monday afternoon.
The first happened at 2.30pm outside the BP petrol station on Keighley Road, Bingley. Two males attempted to rob a G4S driver who had just exited the customer area of the station. One of the males got out of a red Peugeot 307 armed with a weapon believed to be a hatchet whilst one remained inside the vehicle.
They then fled empty handed in the direction of Bingley Main Street in the same vehicle they had arrived in.
Officers want to speak to two men in connection with this incident. They are both described as Asian. The man who got out of the vehicle is described as wearing a dark grey hooded top, dark bottoms and blue Nike Air trainers. He was also wearing a balaclava.
A short time later at 2.49pm officers received reports of a car on fire at Wilsden Old Road at the junction with Narrow Lane in Harden, Bingley. It was established that the vehicle was the one used in the earlier incident.
The second attempted robbery officers are investigating happened at 4.30pm outside the Tesco Express store on Haworth Road, Bradford, less than four miles away.
In this incident two males wearing balaclavas and carrying weapons got out of a dark green Volkswagen Golf and unsuccessfully attempted to get money from a G4S van. It is thought there was a third male who remained in the vehicle.
They then fled empty handed in the Golf along Howarth Road in the direction of the city centre. The car believed to have been involved was located later on Shaftsbury Avenue, Bradford,
The two men who got out of the vehicle are described as wearing dark clothing.
No one was injured in any of the incidents.
Detective Inspector Matthew Walker of Bradford CID, said.
"These are two serious incidents which will have understandably caused concern in the local area and we are doing everything we can to bring those responsible to justice.
"Both incidents happened at busy times of the day and I want to appeal directly to anyone who witnessed anything suspicious to get in touch."
Call Bradford CID on 101."