Thanks to "lefloh" comment - I finally done it!
You have to add these maven dependencies
<dependency>
<groupId>org.jboss.resteasy</groupId>
<artifactId>resteasy-client</artifactId>
<version>3.0.1.Final</version>
</dependency>
<dependency>
<groupId>org.jboss.resteasy</groupId>
<artifactId>resteasy-multipart-provider</artifactId>
<version>3.0.1.Final</version>
</dependency>
And here is the client code:
ResteasyClient client = (ResteasyClient) this.client;
ResteasyWebTarget target = client.target("http://localhost:8080").path("path");
MultipartFormDataOutput mdo = new MultipartFormDataOutput();
mdo.addFormData("firstPart", new ByteArrayInputStream("firstContent".getBytes()), MediaType.TEXT_PLAIN_TYPE);
mdo.addFormData("secondPart", new ByteArrayInputStream("secondContent".getBytes()), MediaType.TEXT_PLAIN_TYPE);
GenericEntity<MultipartFormDataOutput> entity = new GenericEntity<MultipartFormDataOutput>(mdo) { };
Response response = target.request().put(Entity.entity(entity, MediaType.MULTIPART_FORM_DATA_TYPE));
response.close();