In chemistry, Zaitsev's rule, Saytzeff's rule or Saytsev's rule named after Alexander Mikhailovich Zaitsev (number of different spellings due to the name being transliterated from Russian) is a rule that states that if more than one alkene can be formed during dehalogenation by an elimination reaction, the more stable alkene is the major product. In general, the compound that has a more highly substituted C=C double bond is more stable.
He said, "The alkene formed in greatest amount is the one that corresponds to removal of the hydrogen from the β-carbon having the fewest hydrogen substituents."
Another way to state it is as follows: in elimination reactions, the major reaction product is the alkene with the more highly substituted (more stable) double bond. This most-substituted alkene is also the most stable. Under thermodynamic conditions β elimination occurs to form the most stable alkene. This principle is similar to Markovnikov's rule which applies to the reverse process, addition reactions.
The textbooks offer different explanations for the physical origin of the rule. The more-substituted double bond is more stable due to the electron donating properties of the alkyl group . The effect can also be attributed to hyperconjugation with a stabilizing interaction between the HOMO of the alkyl group with the LUMO of the double bond. In terms of orbital hybridization it is noted that C(sp2)-C(sp3) bonds are stronger than C(sp3)-C(sp3) bonds. The higher stability of substituted double bonds can also be inferred from heats of formation. A dominant stabilizing hyperconjugation effect of 6 kcal/mole per alkyl group can be found by computation 
The Zaitsev rule is correct only when there are no other substituents beside carbon and hydrogen. Once other atoms are added; electronegativity, resonance, and other factors complicate the situation and invalidate the rule.
During the elimination reaction, the base that causes the double bond to form has to be sterically unhindered for the reaction to follow Zaitsev. If the base, for example, is (CH3)3CONa, the bulkiness prohibits the base from pulling the leaving group off the most substituted carbon. Another carbon atom is chosen and the Hofmann Product forms.