My slackware version is 13.37. I want to create a iscsi service to share storage to other machine, but I don't find any software supported.

Who can give me some advice?

You're looking for an iSCSI Target.

The Linux kernel has supported the LIO Target since it was merged in January 2011. The choice if LIO over other competing targets was controversial, and the official Wiki page is full of warnings not to use supposedly supported features.

You'll need to download the necessary userspace tools, which right now seems to be targetcli. Some distributions offer it as a package, but AFAIK this is not the case for Slackware.

Alternatively, you could use iSCSI-SCST. It supports several of the features marked as "do not use" in LIO and has been considered stable for years, but to achieve optimal performance you'll unfortunately have to patch the kernel.

(Disclaimer: I'm a longtime SCST user and no fan of LIO.)

I know there are a thousand slackers here but maybe a different distro geared toward enterprise work?

Jefro gets flamed by slackers seeking revenge, runs and hides.

No need to hide, but surely changing distros for a single (and very small) userspace program is a bit overkill?

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As you said, slackware does not native support iscsi storage, so I have to study other linux distros.

Changing a linux distro is easier and cheaper than changing a storage though it is a bit overkill, but is key requirement for me.

I need load and check remote iscsi service.

TargetCLI would be the prime choice for iSCSI support. Even though Slackware doesn't have an official package doesn't mean it can't be installed using a traditional configure-make-install setup. You could even look into drafting a SlackBuild script.