A specialist unit launched the hunt in the city's Broomhouse area following intelligence which indicated weapons were stashed there.
Residents were warned about the operation in leaflets put through the doors of properties in Broomhouse Square and Broomhouse Loan.
Private gardens were cordoned off today as officers combed the areas.
A Lothian and Borders Police spokesman said: "Throughout the day we will be asking residents for permission to access their property, and we will aim to cause as little disruption as possible.
"We are acting on information that there may be firearms hidden within a garden in the area, possibly without the knowledge of the homeowner.
"We are keen for any new information that can assist our inquiries, and rest assured that any calls we receive will be treated in the strictest of confidence."
The force said the activity should serve as a warning to criminals across the capital.
The spokesman said: "Serious and organised criminal groups often use local communities as cover for their activities, and cause misery for the majority of decent law-abiding people who live there.
"Dismantling these groups is a priority for Lothian and Borders Police, and if we receive information that can help us disrupt their activities then rest assured we will take the necessary action required."