With auto insurance claims on the rise, two agencies say their rates are climbing with them.

Bill Mellander of Allstate said their rates, which rose as part of a three-part package, took a hike in Texas in July. In Allstate Indemnity, the rates rose 3.6 percent and in Allstate County Mutual, the rates rose 5.8 percent, Mellander said.

On average, those increases will mean a $4.98 and $7.69 increase, respectively, per customer at Allstate.

“Recently we’ve seen an up-kick in bodily injury expenses and collision expenses. It warrants that the right thing to do...