The SSP's annual conference in Dundee's Caird Hall passed a motion calling for new laws to ban all physical punishment of children.
Steven Johnston, from Edinburgh, who moved the motion, said: "That corporal punishment harms children is not in doubt, although this does challenge traditional Scottish attitudes."
The motion also called for a public education information campaign and increased support for "positive parenting".
However, some delegates warned against making it illegal to smack children.
Graeme McIver, an SSP member from the Borders and a father of four, acknowledged that corporal punishment was "wrong". But he went on: "While we should campaign and argue for parents not to smack their children, we should stop short of criminalising them."
The Scottish Parliament has twice rejected legislation to outlaw smacking, most recently when Labour's Marlyn Glen sought to amend the Family Law Bill last November.
In January, the Children's Commissioner, Kathleen Marshall, joined her three counterparts from the other nations in the UK in calling for a ban.