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Variations of critical temperature $T_c$ and in-plane critical field $H_{c2}$of $\text{Sr}_2\text{Ru}\text{O}_4$ under uniaxial stress have recently beenreported. We compare the strain dependence of $T_c$ and $H_{c2}$ in variouspairing channels ($d$-wave, extended s-wave and $p$-wave) with the experimentalobservations, by studying a three-band tight-binding model that includeseffects of spin-orbit and Zeeman couplings and a separable pairing interaction.Our study helps narrow down the possibility of pairing channels. The importanceof the multi-band nature of $\text{Sr}_2\text{Ru}\text{O}_4$ is alsohighlighted.

$T_c$ and Pauli limited critical field of $\text{Sr}_2\text{Ru}\text{O}_4$: uniaxial strain dependence