The Virginia State Board of Education voted unanimously Thursday to request relief from key parts of the federal No Child Left Behind law, which has drawn widespread criticism for saddling schools with unrealistic achievement goals and harsh penalties.

If Education Secretary Arne Duncan grants Virginia’s request, schools will no longer be required to ensure that all students are proficient in math and reading by 2014.

Instead, Virginia will judge schools according to the state accreditation system, which is based on graduation rates and students’ proficiency on math, language arts, social studies and science tests.

Ninety-six percent of Virginia schools were fully accredited last year, as opposed to the 38 percent deemed successful under No Child Left Behind.

Virginia would also create new “proficiency gap groups” to track the achievement of traditionally underperforming students, including students with disabilities, English language learners, poor children and other minorities.

Advocates for those students have raised concerns that as written, the plan would mask some significant achievement gaps and allow others to go unaddressed.

Congress has offered no legislative fix to No Child Left Behind, despite mounting concerns about its unworkability. In August, Duncan announced that he would unilaterally grant flexibility waivers to states that outline alternative accountability plans and agree to certain education reforms.

Eleven states asked for and received waivers in the first round. Now Virginia is among more than two dozen second-round applicants, including Maryland and the District, whose requests are due by Feb. 28.

Superintendent of Public Instruction Patricia I. Wright said she is optimistic, based on communications with the Education Department in recent weeks, that Virginia’s waiver request will be granted.