It happened in Stratford Road between 11.30pm on Friday (02/10) and 9.10am on Saturday (03/10) when someone broke into a residential garage and stole a TM 250cc EXCTPI euduro motorcycle.
Officers have been investigating, including speaking to neighbours who may have heard something, but now want to hear from the wider public.
PC Andy Windsor, from Salisbury Community Policing Team, said: “We want to hear from anyone who may have seen suspicious activity in the Stratford Road area overnight on Friday, or anyone who may have seen the stolen motorbike for sale.
“Please take a look at the attached photograph, and if you can help in any way then please call us.”
Anyone with information should call Wiltshire Police on 101, quoting crime reference 54200099469.