Beeston, 28, originally from East End Park in Leeds, absconded from HMP Kirklevington Grange, in Yarm, on February 13.
Beeston was jailed for 10 years in 2013 along with three other men who committed a series of armed robberies across West Yorkshire.
Police say Beeston has "connections and associates in east Leeds" and are appealing for help in tracing him.
West Yorkshire Police said: "He is not thought to present any immediate risk to the public but anyone who sees him is advised not to approach him and to contact the police on 999 immediately."
Detective Inspector Phil Jackson, of Leeds Serious Organised Crime Unit, said: “We have searched a number of addresses and are continuing to make extensive enquiries to trace Beeston and return him to prison.
“We are still very keen to hear from anyone who has seen him or who has any information that could assist in tracing him.
“We would like to remind anyone who may be assisting Beeston that it is a criminal offence and they will face serious consequences.”