Outbreaks of rain will also spread across Scotland from the southwest during the early hours of Wednesday morning into Thursday morning.
A Met Office spokesperson said: “Heavy showers and thunderstorms are expected to develop across Scotland during Tuesday afternoon, lasting well into the evening in some places.
"Where these showers occur, 20 to 40 mm of rain is possible in a couple of hours with the potential for around 60 mm in 3 to 6 hours in some locations.
“This may cause localised flooding, especially if such totals occur over urban areas.
"Lightning and hail will pose additional hazards.”
Areas potentially affected by the thunderstorms include Angus, Clackmannanshire, Dundee, Falkirk, Fife, Perth and Kinross, Stirling, Aberdeenshire, Moray, the Highlands, Dumfries and Galloway, East Lothian, Edinburgh, Midlothian Council, Scottish Borders, West Lothian
In the Strathclyde area, Argyll and Bute, East Ayrshire, East Dunbartonshire, East Renfrewshire, Glasgow, North Lanarkshire, Renfrewshire, South Lanarkshire and West Dunbartonshire will also be affected.
There is a chance of delays and some cancellations to train and bus services.
Power cuts might occur and other services to some homes and businesses could be lost.
Spray and sudden flooding could lead to difficult driving conditions and some road closures while some communities might become cut off if roads flood.
Traffic Scotland is urging motorists to drive safe during this weather and to avoid the roads if possible.
Heavy showers on Monday across Scotland may also cause flooding from surface water and small watercourses leading to localised flooding of roads and low-lying land, causing potential travel disruption.
More widespread impacts are expected this week with flood alerts issued for Aberdeen City, Aberdeenshire, Dundee and Angus.
A SEPA spokesperson said: “Remain vigilant and remember, it is your responsibility to take actions which help protect yourself and your property.
"Advice and information is also available through Floodline on 0345 9881188.”