The Katyusha rockets hit areas in the centre of the city, which is encircled by the Shiite Huthi rebels and allied forces loyal to ousted president Ali Abdullah Saleh, a military official said.
He said the rockets were "fired by Huthis and Saleh forces".
"Al-Mutahideen hospital has received 22 bodies of civilians," a medical source said.
The city remains in the hands of forces allied with President Abedrabbo Mansour Hadi.
Human Rights Watch accused the rebels and Saleh's forces today of repeatedly firing mortar shells and artillery rocket "indiscriminately" into populated areas of Taez.
"The pro-Huthi forces should take all possible steps to minimise harm to civilians, end the unlawful confiscation of essential goods from civilians and hold accountable commanders responsible for unlawful attacks," the rights group said.
The Huthis overran the capital Sanaa in September 2014 and went on to seize control of several regions, aided by Saleh's forces.
In July, loyalists backed by a Saudi-led Arab coalition evicted the rebels from five southern provinces and have set their sights on Sanaa.
Around 4,500 civilians have been killed in the conflict since March, when the coalition began targeting the rebels in air strikes.
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