The men, aged 60 and 28, are being investigated in connection with the robbery at the Co-operative Bank on Prospect Crescent just before 1pm on Monday 6 April.
It is reported that threats of violence were made towards a member of staff before a suspect left with a quantity of cash.
The 60 year-old man remains in custody and the 28 year-old man has been released on conditional bail.
Officers have confirmed they are not looking for anyone else in connection with the incident.
They are continuing to appeal for information and are asking witnesses and businesses with CCTV in the area to come forward.
We can confirm that following swift actions by officers two men have been arrested.
We are continuing to appeal for witnesses to this incident.
We know that town was relatively quiet at the time but would urge anybody who saw anything suspicious in this area to contact us.
If anybody saw anything that might help the investigation or has any relevant CCTV or dash-cam footage please contact us on the details below.
Witnesses or anyone with information that could assist the investigation is asked to call North Yorkshire Police on 101, select option 1, and speak to the Force Control Room.
Alternatively, contact Crimestoppers anonymously on 0800 555111.
Please quote reference number 12200056324 when providing details about this incident.