Edinburgh’s tram line was flooded for the first time and the Inverness-Aberdeen railway line was under water in two places.
It came as more rain fell in Edinburgh in two days than the average for the whole of June.
Police said the motorist who died was a 42-year-old man on the A85 two miles east of Gilmerton, near Crieff, on Monday.
A 48-year-old man died in Hampshire yesterday morning in similar conditions.
Tram tracks in Edinburgh were left 3ft under water because of flooding of the A8 underpass between Edinburgh Gateway and Gyle stations, cutting off the depot.
Trams had to be left out on the line overnight and could not run yesterday between Edinburgh Airport and Edinburgh Park.
The first flooding since the line was laid six years ago is being investigated.
The Met Office said 85mm of rain had fallen at the Royal Botanic Garden Edinburgh in the 48 hours to 11am yesterday compared with the 61mm average for the whole of June.
The Borders experienced a similar deluge, with the June average of 78mm falling at Carterhouse near Roxburgh over the same period.
Six homes at Portsoy in Aberdeenshire were flooded, with residents evacuated because of rising water levels.
The Scottish Fire and Rescue Service said it was involved in incidents in Portsoy and Banff, as well as Halkirk in Caithness.
A spokesman said: “A total of six homes have been affected in Soy Avenue and crews are working to divert and alleviate flood waters.”
Schools were closed in Fordyce, Ordiquhill, Portsoy and Whitehills in Aberdeenshire, and Dallas, Mosstowie, Rothiemay and Crossroads primary schools in Moray.
Moray Council said it had delivered sandbags to areas to combat localised flooding.
In Moray, a 35-mile stretch of the Inverness-Aberdeen rail line was closed by flooding between Forres and Keith.
Tracks were engulfed by the River Lossie near Elgin, and between Mulben and Keith.
Twelve flood warnings issued by the Scottish Environment Protection Agency were in force for Keith, Findhorn and Nairn and other parts of Moray and Speyside.
Another area of low pressure is forecast to bring more rain today.