实现多选非常简单: 手动添加一个el-table-column，设type属性为selection即可；默认情况下若内容过多会折行显示，若需要单行显示可以使用show-overflow-tooltip属性，它接受一个Boolean，为true时多余的内容会在 hover 时以 tooltip 的形式显示出来。

<template>
  <el-table
    ref="multipleTable"
    :data="tableData3"
    tooltip-effect="dark"
    style="width: 100%"
    @selection-change="handleSelectionChange">
    <el-table-column
      type="selection"
      width="55">
    </el-table-column>
    <el-table-column
      label="日期"
      width="120">
      <template slot-scope="scope">{{ scope.row.date }}</template>
    </el-table-column>
    <el-table-column
      prop="name"
      label="姓名"
      width="120">
    </el-table-column>
    <el-table-column
      prop="address"
      label="地址"
      show-overflow-tooltip>
    </el-table-column>
  </el-table>
  <div style="margin-top: 20px">
    <el-button @click="toggleSelection([tableData3[1], tableData3[2]])">切换第二、第三行的选中状态</el-button>
    <el-button @click="toggleSelection()">取消选择</el-button>
  </div>
</template>

<script>
  export default {
    data() {
      return {
        tableData3: [{
          date: '2016-05-03',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1518 弄'
        }, {
          date: '2016-05-02',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1518 弄'
        }, {
          date: '2016-05-04',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1518 弄'
        }, {
          date: '2016-05-01',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1518 弄'
        }, {
          date: '2016-05-08',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1518 弄'
        }, {
          date: '2016-05-06',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1518 弄'
        }, {
          date: '2016-05-07',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1518 弄'
        }],
        multipleSelection: []
      }
    },

    methods: {
      toggleSelection(rows) {
        if (rows) {
          rows.forEach(row => {
            this.$refs.multipleTable.toggleRowSelection(row);
          });
        } else {
          this.$refs.multipleTable.clearSelection();
        }
      },
      handleSelectionChange(val) {
        this.multipleSelection = val;
      }
    }
  }
</script>