Officials say 15 homes in Verona sustained severe damage.
The Salvation Army is opening a shelter at Memorial Baptist Church in Verona.
Some homes on Madison's west side were also damaged.
Several counties in the Madison area and to the south will be picking up Tuesday from storm damage.
Dane County was under a Tornado Warning. There were reports of two tornadoes, one in Madison that did damage in the Shorewood Hills neighborhood.
In Verona there was damage to Country View Elementary.
There are many reports of damage from wind and falling trees across Madison.
UW-Platteville is closed Tuesday because of storm damage.
Platteville police say Platteville High School is an emergency shelter for people who were displaced by storm damage.